user6: Let's say that a country decided to ditch their currency and go for Bitcoins. What would this country have to reinvent. The reason why I ask, is because I believe that if a tiny country was to adopt Bitcoins as their official currency, then this would remove all legal issues related to this currency, and hence would enable it to get adopted more widely.
Some of the issues that could require reinventing something could be in relation to:

Transparency requirements for the government to efficiently tackle

Black economy
VAT and general taxation fraud
Financing of terrorism

Ability to peg the currency to other currencies if this is judged as a good idea
Have an efficient banking system
Ability to fight deflation

Any other issues, which I have not thought about. Please note that you do not have to answer all these issues in any one answer, just one of them. 

user118: The short answer is that would have to reinvent bitcoin
In order for a country to adapt a new currency they have to abandon their old currency, this is done by making a law that transfers the value of the source currency to the new currency on a given date at a given rate (which may be decided on the day), but doing this is impossible with bitcoin since there isn't a central authority that can bless this sort of magic transaction as there was with the euro.
Basically they would have to invent a crypto currency that starts with the replacement of the source currency as it's seed.

user32906: There are other practical challenges a country need to face:
Before even starting the change, a government must convince people.
Old people here in Hungary still insist on using cash, and nobody can convince them to use bank cards: they got their salaries on the bank account and the first thing they do is going to the bank and withdraw the entire account as cash.
Also crypto-currencies require internet access. This means every people in the country must have some form of access to the internet to be able to transfer money between each other. So far no country in the world have 100% internet penetration. Here in Hungary the internet penetration is only 75%, this means 2.5 million don't have or don't wish to have access to the internet. 
These people must be served by new system as well. Eg. they should make paper wallets that should be filled up by their employer.
People also need education. If you are careless it's rather easy to wipe off the private key of the current change address from your computer or smart phone and losing all the money.
Also in case of the paper wallets if someone can access their papers for a short time can take the money off from them without actually stealing the paper. 
Authorities must find a way to track people's spendings. Banks nowadays must report the transactions to the tax authorities, so they can claim the right amount of tax. With bitcoin we are basically back the age of cash which is almost untrackable. 
I have no idea how could they accomplish this.
The current Bitcoin system has a fixed money supply.
It doesn't address the problem of lost coins and hoarding.
Without some depreciation there is no incentive to actively exchange it. 
So people instead will hoard it and use it as permanent store of value.
If we want active exchange then we should create a system that encodes some moderate inflation, that's large enough so people don't want store their savings in it, instead they exchange it and buy other financial assets to store value in.

user409: The most likely scenario in which a government would adopt Bitcoin is when their own currency is undergoing hyperinflation. As Gareth's answer points out, there would be no way to transfer the value of the old currency into Bitcoins. But if the currency had essentially no value anyway, it would not have to make that transition. In economies suffering hyperinflation, citizens typically switch to other currencies before their governments. Once the citizens have reached consensus that the old currency is worthless and privately switched to Bitcoins themselves, the government just has to agree to accept Bitcoins as payment, and the transition is complete.

user793: A nation State would never adopt Bitcoin willingly because the government would lose control over the ability to inflate the money supply.  Inflation is nothing more than a tax.  No government will ever willingly give up its primary means of stealing from the public.  The inflation tax is the most insidious and the easiest for government to get away with.  It is much more difficult to force people to hand over their money than it is to simply print new money.  Historical charts of US tax revenue show that no matter what rate the government sets taxes at, revenues always come in at around 20% of GDP.  This means that if the government wants to spend above 20% of GDP they must inflate the money supply as people will simply scam the tax system at higher rates.
Further, it would be ridiculous for any coercively funded government to implement its own version of Bitcoin that they retain control of, because once people found out that an identical open source currency system existed that had no inflation, they would use that system instead.  Once an economy has been restructured to use crypto-currencies, no one in their right mind would chose to use the government issued currency when they could use Bitcoins instead.
Thus, a State implementation of crypto-currency will never occur.  However, because Bitcoin has so many advantages over State issued currency and the fact that its exchange rates can not be controlled by a State, it is highly likely that over time Bitcoin will become the dominate global currency.  This is because taxation can be avoided with Bitcoins, which allows businesses to by-pass legal tender laws. According to Thier's law, in the absence of legal tender laws, good money will drive out bad money.

user117: TL;DR:

In the first instance, my belief is that a government would have to
  create their own brand of Bitcoin (i.e. a new version of the
  blockchain) and use that to trade against other currencies. This is a
  useful move because the government retains control over their currency
  (they set the mining rules) and they don't suffer a wealth drain in
  the process.

In more detail, once a country (our mythical Seashell Island from the earlier draft) has decided that it wants to adopt Bitcoin as it's local currency the following timeline is likely to come into play:
Research into Bitcoin
At this time the government will need to look into what benefits and drawbacks Bitcoin is likely to bring to their economy. Assuming that they currently have a weak currency, then adopting Bitcoin early could be seen as a smart move since it gives them lower cost of entry into the Bitcoin marketplace. 
Among the obvious advantages that Bitcoin brings with it are:

resistance to counterfeiting
resistance to inflation
easier to track than cash for traditional transactions types (i.e. not including private sales of high value private keys)

Some of the drawbacks are:

economy becomes vulnerable to loss of electricity/networking (true of all electronic transactions at present)
banks have a reduced regulatory role since transactions become largely anonymous 
increased potential for anonymous transactions to take place in large amounts

This last drawback is perhaps the most serious since it allows for a vast amount of money to be moved in and out of the country without the knowledge of the government. Admittedly, this happens in the present system although due to the large physical size of cash it usually requires laundering of some kind (conversion to something precious). 
However, government resources are significant and it is very hard to remain anonymous for long. Over time detailed statistics analysing transactions could be used by the police to pinpoint individuals reusing Bitcoin addresses. This process is made much easier by the existence of tools like blockexplorer.com and should be seen as an improvement over the existing traceability processes.
Setting up the necessary processes/contracts to obtain some form of Bitcoin
By this stage the government researchers will likely have determined that there are only a few feasible options to get hold of bitcoins (note the lowercase here):

set up their own mining pool (initially paying for it in their own currency) - unlikely
create a suitable contract with a mining pool to buy a large quantity of bitcoins (without including their own soon to be worthless currency - unlikely 
encourage their citizens to go forth and buy bitcoins themselves and slowly drain the local currency into foreign hands then pull the plug on it (not exactly above board) - unlikely

Using any of the above approaches at this stage requires a significant transfer of wealth from the country into bitcoins and is probably the hardest part to get right. The problem is that there is no central authority who can control the supply of bitcoins exposing the country to the influence of the market. In the case of Euros, the exchange rate of the participating currencies was fixed well in advance after significant negotiation. When the time came to switch over nobody lost out because all the old currency was replaced with the new, which could be printed at will by the central bank. 
It could be argued (by @David Perry for one) that some kind of intermediate value-store could be used, such as gold or silver. However, this still requires all of the country's wealth to be slowly converted to this value-store which will raise eyebrows among those folks selling it in exchange for a soon to be worthless currency. I'd welcome further discussion on this.
There is a significant danger that the country could be declared bankrupt in it's own currency before it is able to complete the operation.
EDIT to cover the most likely path by a government:

if a government made their own blockchain (e.g. SeashellCoin) then they could in theory use scripts to manage trades with Bitcoin. 

This would permit a staged transition and essentially solves the value-store problem. The value of a Seashell would be fixed against their SeashellCoin equivalent (probably as 1:1). In my opinion, this is probably the most likely mechanism that a government could take. The government could decide upon their own inflation model, select a Version entry and then throw a supercomputer on the job for 5 minutes to generate a few million coins. Once that's done then they can take advantage of the blockchain approach and off they go.
Setting up the necessary legislation to make them legal tender locally
Once an adequate number of Bitcoins are, somehow, in the government coffers they can then make the announcement that all local debts can be paid in bitcoins and will be accepted by a court of law. This ratifies Bitcoins around the world (assuming the country is a recognised state) leading to a huge increase in the value of Bitcoins. It also opens the door to taxation in bitcoins which would largely operate in the same way as it did before. 

Value Added Tax (VAT) (aka sales tax) would continue to be added to Bitcoin transactions by merchants who would then transfer the money to the government at regular intervals, overseen by accountants
Income tax would also stay the same 
Accounts would have to be returned along with their transaction IDs to allow verification of truth
Standard statistical methods to detect fraud would remain (relies on most folks behaving themselves)

Managing the transition among the general population
Since it is the government driving this then they are likely to provide all necessary equipment to facilitate the transfer. This would include:

recommendations for mobile phone applications (probably not likely to make their own due to "backdoor" privacy concerns)
provision of Bitcoin Wallet Devices that offer tamperproof private keys and are essentially like smartphones for those that don't have mobile phones (see the original Fred)
provision of EPOS systems that are Bitcoin enabled 

All of the above would probably occur via contracts with private companies. 
Handled well, the transition to Bitcoin would be like introducing a new contactless payment system. They would still want to maintain a secure location for their bitcoins (most likely a government backed bank) and after a while it would just fade into the background. 
Reaping the benefits to the economy afterwards
Much of the long term benefits would stem from

the decreased transaction friction within the existing legal and banking system
better fiscal policy since supply is limited leading to improved standards of living and quality of life
increased long term wealth as an early adopter to a global currency
greater transparency in accounting that can be easily verified
immunity to global currency crises

Just my 2 BTCs.

6: <p>Let's say that a country decided to ditch their currency and go for Bitcoins. What would this country have to reinvent. The reason why I ask, is because I believe that if a tiny country was to adopt Bitcoins as their official currency, then this would remove all legal issues related to this currency, and hence would enable it to get adopted more widely.</p>

<p>Some of the issues that could require reinventing something could be in relation to:</p>

<ul>
<li>Transparency requirements for the government to efficiently tackle
<ul>
<li>Black economy</li>
<li>VAT and general taxation fraud</li>
<li>Financing of terrorism</li>
</ul></li>
<li>Ability to peg the currency to other currencies if this is judged as a good idea</li>
<li>Have an efficient banking system</li>
<li>Ability to fight deflation</li>
</ul>

<p>Any other issues, which I have not thought about. Please note that you do not have to answer all these issues in any one answer, just one of them. </p>
 118: <p>The short answer is that would have to reinvent <strong>bitcoin</strong></p>

<p>In order for a country to adapt a new currency they have to abandon their old currency, this is done by making a law that transfers the value of the source currency to the new currency on a given date at a given rate (which may be decided on the day), but doing this is impossible with bitcoin since there isn't a central authority that can bless this sort of magic transaction as there was with the euro.</p>

<p>Basically they would have to invent a crypto currency that starts with the replacement of the source currency as it's seed.</p>
 32906: <p>There are other practical challenges a country need to face:</p>

<p>Before even starting the change, a government must convince people.
Old people here in Hungary still insist on using cash, and nobody can convince them to use bank cards: they got their salaries on the bank account and the first thing they do is going to the bank and withdraw the entire account as cash.
Also crypto-currencies require internet access. This means every people in the country must have some form of access to the internet to be able to transfer money between each other. So far no country in the world have 100% internet penetration. Here in Hungary the internet penetration is only 75%, this means 2.5 million don't have or don't wish to have access to the internet. </p>

<p>These people must be served by new system as well. Eg. they should make paper wallets that should be filled up by their employer.</p>

<p>People also need education. If you are careless it's rather easy to wipe off the private key of the current change address from your computer or smart phone and losing all the money.
Also in case of the paper wallets if someone can access their papers for a short time can take the money off from them without actually stealing the paper. </p>

<p>Authorities must find a way to track people's spendings. Banks nowadays must report the transactions to the tax authorities, so they can claim the right amount of tax. With bitcoin we are basically back the age of cash which is almost untrackable. 
I have no idea how could they accomplish this.</p>

<p>The current Bitcoin system has a fixed money supply.
It doesn't address the problem of lost coins and hoarding.
Without some depreciation there is no incentive to actively exchange it. 
So people instead will hoard it and use it as permanent store of value.
If we want active exchange then we should create a system that encodes some moderate inflation, that's large enough so people don't want store their savings in it, instead they exchange it and buy other financial assets to store value in.</p>
 409: <p>The most likely scenario in which a government would adopt Bitcoin is when their own currency is undergoing hyperinflation. As Gareth's answer points out, there would be no way to transfer the value of the old currency into Bitcoins. But if the currency had essentially no value anyway, it would not have to make that transition. In economies suffering hyperinflation, citizens typically switch to other currencies before their governments. Once the citizens have reached consensus that the old currency is worthless and privately switched to Bitcoins themselves, the government just has to agree to accept Bitcoins as payment, and the transition is complete.</p>
 793: <p>A nation State would never adopt Bitcoin willingly because the government would lose control over the ability to inflate the money supply.  Inflation is nothing more than a tax.  No government will ever willingly give up its primary means of stealing from the public.  The inflation tax is the most insidious and the easiest for government to get away with.  It is much more difficult to force people to hand over their money than it is to simply print new money.  Historical charts of US tax revenue show that no matter what rate the government sets taxes at, revenues always come in at around 20% of GDP.  This means that if the government wants to spend above 20% of GDP they must inflate the money supply as people will simply scam the tax system at higher rates.</p>

<p>Further, it would be ridiculous for any coercively funded government to implement its own version of Bitcoin that they retain control of, because once people found out that an identical open source currency system existed that had no inflation, they would use that system instead.  Once an economy has been restructured to use crypto-currencies, no one in their right mind would chose to use the government issued currency when they could use Bitcoins instead.</p>

<p>Thus, a State implementation of crypto-currency will never occur.  However, because Bitcoin has so many advantages over State issued currency and the fact that its exchange rates can not be controlled by a State, it is highly likely that over time Bitcoin will become the dominate global currency.  This is because taxation can be avoided with Bitcoins, which allows businesses to by-pass legal tender laws. <a href="http://en.wikipedia.org/wiki/Gresham%27s_law#Reverse_of_Gresham.27s_Law_.28Thiers.27_Law.29">According to Thier's law</a>, in the absence of legal tender laws, good money will drive out bad money.</p>
 117: <p>TL;DR:</p>

<blockquote>
  <p>In the first instance, my belief is that a government would have to
  create their own brand of Bitcoin (i.e. a new version of the
  blockchain) and use that to trade against other currencies. This is a
  useful move because the government retains control over their currency
  (they set the mining rules) and they don't suffer a wealth drain in
  the process.</p>
</blockquote>

<p>In more detail, once a country (our mythical Seashell Island from the earlier draft) has decided that it wants to adopt Bitcoin as it's local currency the following timeline is likely to come into play:</p>

<p><strong>Research into Bitcoin</strong></p>

<p>At this time the government will need to look into what benefits and drawbacks Bitcoin is likely to bring to their economy. Assuming that they currently have a weak currency, then adopting Bitcoin early could be seen as a smart move since it gives them lower cost of entry into the Bitcoin marketplace. </p>

<p>Among the obvious advantages that Bitcoin brings with it are:</p>

<ul>
<li>resistance to counterfeiting</li>
<li>resistance to inflation</li>
<li>easier to track than cash for traditional transactions types (i.e. not including private sales of high value private keys)</li>
</ul>

<p>Some of the drawbacks are:</p>

<ul>
<li>economy becomes vulnerable to loss of electricity/networking (true of all electronic transactions at present)</li>
<li>banks have a reduced regulatory role since transactions become largely anonymous </li>
<li>increased potential for anonymous transactions to take place in large amounts</li>
</ul>

<p>This last drawback is perhaps the most serious since it allows for a vast amount of money to be moved in and out of the country without the knowledge of the government. Admittedly, this happens in the present system although due to the large physical size of cash it usually requires laundering of some kind (conversion to something precious). </p>

<p>However, government resources are significant and it is very hard to remain anonymous for long. Over time detailed statistics analysing transactions could be used by the police to pinpoint individuals reusing Bitcoin addresses. This process is made much easier by the existence of tools like blockexplorer.com and should be seen as an improvement over the existing traceability processes.</p>

<p><strong>Setting up the necessary processes/contracts to obtain some form of Bitcoin</strong></p>

<p>By this stage the government researchers will likely have determined that there are only a few feasible options to get hold of <strong>bitcoins</strong> (note the lowercase here):</p>

<ul>
<li>set up their own mining pool (initially paying for it in their own currency) - unlikely</li>
<li>create a suitable contract with a mining pool to buy a large quantity of bitcoins (without including their own soon to be worthless currency - unlikely </li>
<li>encourage their citizens to go forth and buy bitcoins themselves and slowly drain the local currency into foreign hands then pull the plug on it (not exactly above board) - unlikely</li>
</ul>

<p>Using any of the above approaches at this stage requires a significant transfer of wealth from the country into bitcoins and is probably the hardest part to get right. The problem is that there is no central authority who can control the supply of bitcoins exposing the country to the influence of the market. In the case of Euros, the exchange rate of the participating currencies was fixed well in advance after significant negotiation. When the time came to switch over nobody lost out because all the old currency was replaced with the new, which could be printed at will by the central bank. </p>

<p>It could be argued (by @David Perry for one) that some kind of intermediate value-store could be used, such as gold or silver. However, this still requires all of the country's wealth to be slowly converted to this value-store which will raise eyebrows among those folks selling it in exchange for a soon to be worthless currency. I'd welcome further discussion on this.</p>

<p>There is a significant danger that the country could be declared bankrupt in it's own currency before it is able to complete the operation.</p>

<p><strong>EDIT to cover the most likely path by a government:</strong></p>

<ul>
<li>if a government <a href="https://en.bitcoin.it/wiki/Alternative_Chains">made their own blockchain</a> (e.g. SeashellCoin) then they could in theory <a href="https://en.bitcoin.it/wiki/Contracts#Example_5%3a_Trading_across_chains">use scripts to manage trades with Bitcoin</a>. </li>
</ul>

<p>This would permit a staged transition and essentially solves the value-store problem. The value of a Seashell would be fixed against their SeashellCoin equivalent (probably as 1:1). In my opinion, this is probably the most likely mechanism that a government could take. The government could decide upon their own inflation model, select a Version entry and then throw a supercomputer on the job for 5 minutes to generate a few million coins. Once that's done then they can take advantage of the blockchain approach and off they go.</p>

<p><strong>Setting up the necessary legislation to make them legal tender locally</strong></p>

<p>Once an adequate number of Bitcoins are, somehow, in the government coffers they can then make the announcement that all local debts can be paid in bitcoins and will be accepted by a court of law. This ratifies Bitcoins around the world (assuming the country is a recognised state) leading to a huge increase in the value of Bitcoins. It also opens the door to taxation in bitcoins which would largely operate in the same way as it did before. </p>

<ul>
<li>Value Added Tax (VAT) (aka sales tax) would continue to be added to Bitcoin transactions by merchants who would then transfer the money to the government at regular intervals, overseen by accountants</li>
<li>Income tax would also stay the same </li>
<li>Accounts would have to be returned <strong>along with their transaction IDs to allow verification of truth</strong></li>
<li>Standard statistical methods to detect fraud would remain (relies on most folks behaving themselves)</li>
</ul>

<p><strong>Managing the transition among the general population</strong></p>

<p>Since it is the government driving this then they are likely to provide all necessary equipment to facilitate the transfer. This would include:</p>

<ul>
<li>recommendations for mobile phone applications (probably not likely to make their own due to "backdoor" privacy concerns)</li>
<li>provision of Bitcoin Wallet Devices that offer tamperproof private keys and are essentially like smartphones for those that don't have mobile phones (see the original Fred)</li>
<li>provision of EPOS systems that are Bitcoin enabled </li>
</ul>

<p>All of the above would probably occur via contracts with private companies. </p>

<p>Handled well, the transition to Bitcoin would be like introducing a new contactless payment system. They would still want to maintain a secure location for their bitcoins (most likely a government backed bank) and after a while it would just fade into the background. </p>

<p><strong>Reaping the benefits to the economy afterwards</strong></p>

<p>Much of the long term benefits would stem from</p>

<ul>
<li>the decreased transaction friction within the existing legal and banking system</li>
<li>better fiscal policy since supply is limited leading to improved standards of living and quality of life</li>
<li>increased long term wealth as an early adopter to a global currency</li>
<li>greater transparency in accounting that can be easily verified</li>
<li>immunity to global currency crises</li>
</ul>

<p>Just my 2 BTCs.</p>
