user894: Does each bitcoin has a unique identifier, like currency notes have serial numbers? If so, could you trace a particular bitcoin's ownership chain (ie find the current owner of a particular bitcoin by its identifier)? The answer I'm finding is no:

There are also specific features of Bitcoin that make this difficult. Transactions put all the input Bitcoins into a big pile which they dole out as outputs. There's no concept of particular output Bitcoins corresponding to particular inputs. Bitcoins don't have a serial number that can be traced through the block chain. So any such tracking rules would be basically arbitrary.
https://bitcoin.stackexchange.com/a/2139/894

Is this accurate?

user1910: Bitcoins are like fungible realestate.  Your public address owns "title" to a specific fungible quantity of bitcoin.  There are no serialized Bitcoin"s" or individual tokens. When you spend some bitcoin you "deed" a specified fungible amount to the new public address using your private key.  Private keys are stored in your "wallet", which is really just a key safe.  Everyones' balance is stored in the "block chain", which is a public database of all transactions.  Think of the block chain as like a realestate "registrar".  New "grant deeds" of (currently) 50 bitcoin are granted to the "miner" who first solves the hash of the next block.  Solving the hash is computationally difficult and prevents counterfeiting.

user888: Think of how bitcoins are created - in lumps of 50 in a block. You cannot tell the difference between the 'first' bitcoin of this lump of 50 or the 'second' or the 'twenty second'.  It is just a number in a public ledger called the blockchain. There are no serial numbers like on a dollar note. 

user662: If you are asking if Bitcoins can be traced, then answer is no.  If you're asking if public keys can be traced, then the answer is yes.

user409: There is actually no such thing as a bitcoin - there are only transactions, which are denominated in bitcoins. Those transactions do have a history, though as the linked answer states, that history can be complex.

user575: Bitcoins are somewhat fungible, but not completely. It's like a family tree. You can't say "this bitcoin was at location Y 2 years ago" any more than you can say "Person X was 1000 years ago person Y". But you can say "This Bitcoin can be traced back to this transaction from 2 years ago" just like you can say "Person Y who lived 1000 years ago is an ancestor of person X".
Just like a person can have millions of ancestors and descendants, so can a bitcoin trace back or forward to millions of bitcoins. But since some bitcoins can be traced back to a particular transaction/address and some cannot, they are not completely fungible, and different bitcoins may be worth more or less.
Here is an example of someone offering to pay 2 "ordinary" bitcoins for 1 bitcoin that can be traced back to the historic transaction of buying pizza for 10K BTC.

user323: That is accurate. Let me start explaining how Bitcoins work from the beginning:

Bitcoins are first created when they are mined by solving a block. The first transaction in the block is basically you saying "I'm giving myself 50 Bitcoins to my address A" (plus transaction fees from the block).
When you want to spend Bitcoins, you have to point to one or more transactions that show where you got them from, and say how many Bitcoins you are transferring where. It's like saying "I got Bitcoins at transaction X. I'm sending 20 coins to address B."
The point is that more often than not you don't want to send all the coins you got from the transaction, so you also specify how much change you are sending to another address, usually controlled by yourself: "I got Bitcoins at transaction X. I'm sending 20 coins to address B and 30 coins to address A."
Since all of the above is cryptographically signed, one can be sure nobody can spend coins they don't have (spending more than they have, spending someone else's coins, etc).
To make sure nobody is cheating, everyone is looking at everyone's hands by checking each transaction that comes their way. If you cheat, your transaction does not get forwarded.

I hope that explains the concept of how Bitcoin works in regards to your question. Just to be clear:
"Does each bitcoin has a unique identifier, like currency notes have serial numbers?"
Not like currency (that each bill has a serial number and you can't break them apart), more like bank statements (the identifier identifies the transaction on a certain amount of Bitcoins), but that's still a simplification.
"If so, could you trace a particular bitcoin's ownership chain (ie. find the current owner of a particular bitcoin by its identifier)?"
You can trace the history of transactions on the set of Bitcoins up to who mined them, but not on a particular 1BTC. It's like saying "Alice paid Jill $10. Jill got $20 from Bob. Bob got $50 from the mint."

894: <p>Does each bitcoin has a unique identifier, like currency notes have serial numbers? If so, could you trace a particular bitcoin's ownership chain (ie find the current owner of a particular bitcoin by its identifier)? The answer I'm finding is no:</p>

<blockquote>
  <p>There are also specific features of Bitcoin that make this difficult. Transactions put all the input Bitcoins into a big pile which they dole out as outputs. There's no concept of particular output Bitcoins corresponding to particular inputs. Bitcoins don't have a serial number that can be traced through the block chain. So any such tracking rules would be basically arbitrary.</p>
  
  <p><a href="https://bitcoin.stackexchange.com/a/2139/894">https://bitcoin.stackexchange.com/a/2139/894</a></p>
</blockquote>

<p>Is this accurate?</p>
 1910: <p>Bitcoins are like fungible realestate.  Your public address owns "title" to a specific fungible quantity of bitcoin.  There are no serialized Bitcoin"s" or individual tokens. When you spend some bitcoin you "deed" a specified fungible amount to the new public address using your private key.  Private keys are stored in your "wallet", which is really just a key safe.  Everyones' balance is stored in the "block chain", which is a public database of all transactions.  Think of the block chain as like a realestate "registrar".  New "grant deeds" of (currently) 50 bitcoin are granted to the "miner" who first solves the hash of the next block.  Solving the hash is computationally difficult and prevents counterfeiting.</p>
 888: <p>Think of how bitcoins are created - in lumps of 50 in a block. You cannot tell the difference between the 'first' bitcoin of this lump of 50 or the 'second' or the 'twenty second'.  It is just a number in a public ledger called the blockchain. There are no serial numbers like on a dollar note. </p>
 662: <p>If you are asking if Bitcoins can be traced, then answer is no.  If you're asking if public keys can be traced, then the answer is yes.</p>
 409: <p>There is actually no such thing as a bitcoin - there are only transactions, which are denominated in bitcoins. Those transactions do have a history, though as the linked answer states, that history can be complex.</p>
 575: <p>Bitcoins are somewhat fungible, but not completely. It's like a family tree. You can't say "this bitcoin was at location Y 2 years ago" any more than you can say "Person X was 1000 years ago person Y". But you can say "This Bitcoin can be traced back to this transaction from 2 years ago" just like you can say "Person Y who lived 1000 years ago is an ancestor of person X".</p>

<p>Just like a person can have millions of ancestors and descendants, so can a bitcoin trace back or forward to millions of bitcoins. But since some bitcoins can be traced back to a particular transaction/address and some cannot, they are not completely fungible, and different bitcoins may be worth more or less.</p>

<p><a href="https://bitcointalk.org/index.php?topic=9238.0">Here</a> is an example of someone offering to pay 2 "ordinary" bitcoins for 1 bitcoin that can be traced back to the historic transaction of buying pizza for 10K BTC.</p>
 323: <p>That is accurate. Let me start explaining how Bitcoins work from the beginning:</p>

<ol>
<li>Bitcoins are first created when they are mined by solving a block. The first transaction in the block is basically you saying "I'm giving myself 50 Bitcoins to my address A" (plus transaction fees from the block).</li>
<li>When you want to spend Bitcoins, you have to point to one or more transactions that show where you got them from, and say how many Bitcoins you are transferring where. It's like saying "I got Bitcoins at transaction X. I'm sending 20 coins to address B."</li>
<li>The point is that more often than not you don't want to send all the coins you got from the transaction, so you also specify how much change you are sending to another address, usually controlled by yourself: "I got Bitcoins at transaction X. I'm sending 20 coins to address B and 30 coins to address A."</li>
<li>Since all of the above is cryptographically signed, one can be sure nobody can spend coins they don't have (spending more than they have, spending someone else's coins, etc).</li>
<li>To make sure nobody is cheating, everyone is looking at everyone's hands by checking each transaction that comes their way. If you cheat, your transaction does not get forwarded.</li>
</ol>

<p>I hope that explains the concept of how Bitcoin works in regards to your question. Just to be clear:</p>

<p>"Does each bitcoin has a unique identifier, like currency notes have serial numbers?"</p>

<p>Not like currency (that each bill has a serial number and you can't break them apart), more like bank statements (the identifier identifies the transaction on a certain amount of Bitcoins), but that's still a simplification.</p>

<p>"If so, could you trace a particular bitcoin's ownership chain (ie. find the current owner of a particular bitcoin by its identifier)?"</p>

<p>You can trace the history of transactions on the set of Bitcoins up to who mined them, but not on a particular 1BTC. It's like saying "Alice paid Jill $10. Jill got $20 from Bob. Bob got $50 from the mint."</p>
