user4432: What happens when bitcoins loans start to appear? 
Loans have interest rates that "create additional value". Given the limited amount of bitcoins, couldn't we realistically run out of them?
BitBanker loans 1000BTC to the user with a 5% interest. The loan could be backed up with, say, a house.
The user then has to pay back 1050BTC, somehow acquiring the 50BTC deficit.
Given how quickly interest on top of interest grows, won't the bankers get to 21 million BTC quite quickly?

user2306: 
Given how quickly intrest on top of intrest grows, won't the bankers get to 21 million BTC quite quickly?

Sure, but is that really meaningful? Let's say that I loan you 1 BTC, with the terms that I get 10% interest per day. Before the year is out, you owe me more bitcoins that actually exist. The face value is the amount that the loan is supposed to be worth, if everybody keeps their word. 
However, the real value is much lower - you're a random stranger on the internet, and you're unlikely to come up with quadrillions of dollars. 
Bitcoin can't save you from untrustworthy borrowers.

user1307: If bankers would, by giving out loans and the interests on them, transcend the actual number of bitcoins existing, what is the difference with the current banking system?
In most countries, there is also more money in circulation through banks and loans than there actually exists. And it was just so when the gold standard still existed.
That's just how these economic systems work. The only difference is that when bitcoin banks would fail, they cannot, or hardly, be saved by governments.
Besides, wouldn't such a situation contradict the spirit that makes bitcoin so popular? Bitcoin is about doing away with bankers and the corruption they are associated with. Bitcoin is about not having to trust someone else that gives you some money and tells you that it has value. 

user4477: 
Loans have intrest rates that "create additional value". Given the limited amount of bitcoins, couldn't we realistically run out of them?

No, you wouldn't run out of Bitcoins for the simple fact that they will always be traded. Your interest payments on your loan would come out of Bitcoin trading that you did to increase your Bitcoins, even if you only did Bitcoin trading to repay your loan.
If ALL Bitcoin holders became hoarders, the price of Bitcoins would increase as more and more people wanted some. Bitcoin, if as rare as gold and jewels, becomes more valuable. Finally, when the "price" of Bitcoins was high enough, some hoarders would trade theirs off for fiat currencies, just like gold and silver.
People or companies who loan Bitcoin need to be as careful as those who borrow them. If a lender lends when the Bitcoin price is high, and then the Bitcoin price drops, it will be much more easier for the borrower to "purchase" more bitcoins to pay off the loan. This may be adverse to the lender's financial plan.
On the other hand, if the borrower borrows when the price is low, and then the price goes way up, the borrower might be scrambling just to make payments so that he doesn't lose the house, and his proverbial shirt.
As Bitcoin becomes more commonplace, there might come into being "holding houses" that hold the paper on property that secures the loans that lenders make.

user58615: None of the above really answers your question. To understand the answer, we have to first understand the main difference between a fiat currency like USD and Bitcoin which is fixed in amount, just like gold.
In fiat currencies like USD, the amount/quantity of money is unlimited, i.e. banks can create new money out of thin air. So when banks give loans, they create new money out of thin air and charge a positive interest rate on it. Remember that this interest amount does not exist in the economy when the loan is taken/given and the interest amounts' worth of money/notes/coins are also created by banks from thin air. So in fiat currencies, the value of each unit of money goes down as time passes because the amount of money/notes/coins is being increased every day and so everybody has more amount of money/notes/coins with each passing day. A dollar tomorrow will buy less goods/services than it can today and so on.
In a fixed amount currency like bitcoins, as people borrow bitcoins from others, the value of each unit of bitcoin goes up as time passes. This is because there is a fixed number of bitcoins available and more people demanding more bitcoins through loans will mean every unit of bitcoin is valued more. So in bitcoin loans, the interest rates will be negative. That is, if I give you a loan of 1 BTC and charge -10% interest rate on it, I will actually pay YOU 0.1 BTC every year! It's the exact reverse of the fiat currency system.
Now in a fiat currency economy, if the inflation rate is say 5%, and banks charge 12% interest on loans, they beat inflation by approximately 7% every year which is their profit. 
In the Bitcoin system, if the "deflation" rate is -15% and banks loan at an interest rate of -10%, they make a profit of -10% - (-15%) = 5%. In simple terms, while the rest of the bitcoin holders have to give away 15% of their bitcoins every year due to deflation, the bank have to give only 10% of their bitcoins, thus saving 5% every year.

4432: <p>What happens when bitcoins loans start to appear? </p>

<p>Loans have interest rates that "create additional value". Given the limited amount of bitcoins, couldn't we realistically run out of them?</p>

<p>BitBanker loans 1000BTC to the user with a 5% interest. The loan could be backed up with, say, a house.</p>

<p>The user then has to pay back 1050BTC, somehow acquiring the 50BTC deficit.</p>

<p>Given how quickly interest on top of interest grows, won't the bankers get to 21 million BTC quite quickly?</p>
 2306: <blockquote>
  <p>Given how quickly intrest on top of intrest grows, won't the bankers get to 21 million BTC quite quickly?</p>
</blockquote>

<p>Sure, but is that really meaningful? Let's say that I loan you 1 BTC, with the terms that I get 10% interest per day. Before the year is out, you owe me more bitcoins that actually exist. The <em>face value</em> is the amount that the loan is supposed to be worth, if everybody keeps their word. </p>

<p>However, the <em>real value</em> is much lower - you're a random stranger on the internet, and you're unlikely to come up with quadrillions of dollars. </p>

<p>Bitcoin can't save you from untrustworthy borrowers.</p>
 1307: <p>If bankers would, by giving out loans and the interests on them, transcend the actual number of bitcoins existing, what is the difference with the current banking system?</p>

<p>In most countries, there is also more money in circulation through banks and loans than there actually exists. And it was just so when the <a href="http://en.wikipedia.org/wiki/Gold_standard" rel="nofollow">gold standard</a> still existed.</p>

<p>That's just how these economic systems work. The only difference is that when bitcoin banks would fail, they cannot, or hardly, be saved by governments.</p>

<p>Besides, wouldn't such a situation contradict the spirit that makes bitcoin so popular? Bitcoin is about doing away with bankers and the corruption they are associated with. Bitcoin is about not having to trust someone else that gives you some money and tells you that it has value. </p>
 4477: <blockquote>
  <p>Loans have intrest rates that "create additional value". Given the limited amount of bitcoins, couldn't we realistically run out of them?</p>
</blockquote>

<p>No, you wouldn't run out of Bitcoins for the simple fact that they will always be traded. Your interest payments on your loan would come out of Bitcoin trading that you did to increase your Bitcoins, even if you only did Bitcoin trading to repay your loan.</p>

<p>If ALL Bitcoin holders became hoarders, the price of Bitcoins would increase as more and more people wanted some. Bitcoin, if as rare as gold and jewels, becomes more valuable. Finally, when the "price" of Bitcoins was high enough, some hoarders would trade theirs off for fiat currencies, just like gold and silver.</p>

<p>People or companies who loan Bitcoin need to be as careful as those who borrow them. If a lender lends when the Bitcoin price is high, and then the Bitcoin price drops, it will be much more easier for the borrower to "purchase" more bitcoins to pay off the loan. This may be adverse to the lender's financial plan.</p>

<p>On the other hand, if the borrower borrows when the price is low, and then the price goes way up, the borrower might be scrambling just to make payments so that he doesn't lose the house, and his proverbial shirt.</p>

<p>As Bitcoin becomes more commonplace, there might come into being "holding houses" that hold the paper on property that secures the loans that lenders make.</p>
 58615: <p>None of the above really answers your question. To understand the answer, we have to first understand the main difference between a fiat currency like USD and Bitcoin which is fixed in amount, just like gold.</p>

<p>In fiat currencies like USD, the amount/quantity of money is unlimited, i.e. banks can create new money out of thin air. So when banks give loans, they create new money out of thin air and charge a positive interest rate on it. Remember that this interest amount does not exist in the economy when the loan is taken/given and the interest amounts' worth of money/notes/coins are also created by banks from thin air. So in fiat currencies, the value of each unit of money goes down as time passes because the amount of money/notes/coins is being increased every day and so everybody has more amount of money/notes/coins with each passing day. A dollar tomorrow will buy less goods/services than it can today and so on.</p>

<p>In a fixed amount currency like bitcoins, as people borrow bitcoins from others, the value of each unit of bitcoin goes up as time passes. This is because there is a fixed number of bitcoins available and more people demanding more bitcoins through loans will mean every unit of bitcoin is valued more. So in bitcoin loans, the interest rates will be negative. That is, if I give you a loan of 1 BTC and charge -10% interest rate on it, I will actually pay YOU 0.1 BTC every year! It's the exact reverse of the fiat currency system.
Now in a fiat currency economy, if the inflation rate is say 5%, and banks charge 12% interest on loans, they beat inflation by approximately 7% every year which is their profit. 
In the Bitcoin system, if the "deflation" rate is -15% and banks loan at an interest rate of -10%, they make a profit of -10% - (-15%) = 5%. In simple terms, while the rest of the bitcoin holders have to give away 15% of their bitcoins every year due to deflation, the bank have to give only 10% of their bitcoins, thus saving 5% every year.</p>
