user22: For example, if I wanted to "collect" important bitcoins is there any way to track a coin rather than a series of transactions? If I wanted one of the bitcoins from the infamous "Bitcoin pizza" purchase, for example, is there any way to do so?
Perhaps the question I should be asking is more like "Do bitcoins themselves even exist or just the records of transactions?"

user1304: You might want to have a look at the concepts of "taint" and "colored coins". You can start here:
Taint: https://bitcointalk.org/index.php?topic=92416.0
Colored Coins: https://bitcointalk.org/index.php?topic=106373.0

user2157: If you know the TX number, you can go to blockchain.info, search the TX number, click "View Tree Chart" and a tree chart will show up and you can click on the yellow/orange circles. That is how I found out a bitcoin I sent to an exchange ended up plying ping-pong with SatoshiDice.

user85: The simplest way to understand why the answer is "no" is to understand a very basic concept about Bitcoin transactions:
Each transaction (except generating transactions) has one or more "inputs" that pull in Bitcoins. And each transaction has one or more "outputs" that offer those Bitcoins.
In the transaction itself, all the Bitcoins pulled in form a pile. There is no way to track a particular input to a particular output, nor is that meaningful.
Imagine a transaction pulls in 25 Bitcoins from one place and 25 Bitcoins from another place and then sends out 10 Bitcoins to each of five different places. What does it mean to ask which input the coins in a particular output came from?
Bitcoins are more like account balances than pennies. If you put 10 pennies in a pile and give 1 out, you can ask which penny they got. But if you deposit two $10 checks and then withdraw $5, which check did that $5 come from? It's not even a meaningful question.

user81: This is actually similar to the "Can a bitcoin be counterfeited?" question.
The answer is no, because as you seemed to hint at, there is no such thing as a bitcoin. There is simply a transaction list, that has consensus around it, where no wallets are ever allowed to go negative.

user659: I've been playing with Gavin's "bitcointools" (again) to track what happened to the famous "pizza" Bitcoins.
It turns out that rather than being rare collector's items, the 10,000 BTC exchanged for two pizzas have spread out to over a million different Bitcoin addresses since buying the pizzas, not counting the dilute fragments that ended up in transaction fees.
As of block 166149, on Feb 10th 2012, 1,037,382 addresses have held the pizza coins since they were spent.  174,584 of those still hold pizza coins (the others may or may not be empty addresses, since it's possible to have two different transactions output to the same address without the coins becoming mixed together.  In other words it's possible to have "pizza coins" and "non pizza coins" in the same address and still be able to tell which are which.  Of the approximately 600k addresses which are currently holding funds, around 29% of them contain pizza coins.
The shortest chain of transactions from the pizza purchase to currently held pizza coins has length 9, and the longest has length 6,723.
There is no currently unredeemed output which contains 100% pure pizza coins.  All the pizza coins have been diluted somewhat with other coins.  The purest remaining are these 100 BTC which are 90.7276% pure pizza coin, and just 11 transactions separated from the pizza transaction.  (The most recent 9 transactions each only have 1 input, so it's easy to follow it back that far.  In the next transaction back the pizza coins came from both the last but one input, worth 4223 BTC, and 5th from last input, worth 5777.  Together those 2 inputs make up the full 100% pure 10k BTC pizza coins.  The other inputs in this big transaction, worth 1022 BTC in total are the only non pizza coins introduced.  10000 * 100 / 11022 = 90.7276%, the purity). 
I also checked my wallet to see if I was holding any pizza coins.  8 of my addresses are holding pizza coins, but very diluted.  My 'strongest' has a purity of 1.1760%, and is a tiny withdrawal I made from MtGox in October 2011.
Finally, here's some data showing the month-by-month spread of the pizza coins:
pizza payment of 10000.00000000 BTC to 17SkEw2md5avVNyYgj6RiXuQKNwkXaxFyQ
is in block 57043

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
 58815  May 2010          4         2 (50.00%)         4  100.00%  200.00%
 63561  Jun 2010          4         2 (50.00%)         0    0.00%    0.00%
 71436  Jul 2010         26         8 (30.77%)        24   92.31%  300.00%
 77452  Aug 2010         34        10 (29.41%)        13   38.24%  130.00%
 82997  Sep 2010        138        37 (26.81%)       106   76.81%  286.49%
 88892  Oct 2010      2,016       265 (13.14%)     1,898   94.15%  716.23%
 94801  Nov 2010      6,295       577 ( 9.17%)     4,428   70.34%  767.42%
100409  Dec 2010      7,510       835 (11.12%)     1,464   19.49%  175.33%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
105570  Jan 2011     13,271     1,540 (11.60%)     6,150   46.34%  399.35%
111136  Feb 2011     19,055     2,632 (13.81%)     6,423   33.71%  244.03%
116038  Mar 2011     42,027     5,605 (13.34%)    24,341   57.92%  434.27%
121126  Apr 2011     69,544     9,085 (13.06%)    29,727   42.75%  327.21%
127865  May 2011    123,997    26,032 (20.99%)    57,911   46.70%  222.46%
134121  Jun 2011    249,138    54,047 (21.69%)   132,348   53.12%  244.88%
139035  Jul 2011    382,845    93,928 (24.53%)   146,156   38.18%  155.60%
143408  Aug 2011    494,140   108,340 (21.92%)   126,134   25.53%  116.42%
147565  Sep 2011    589,942   119,491 (20.25%)   111,178   18.85%   93.04%
151314  Oct 2011    680,787   131,370 (19.30%)   105,320   15.47%   80.17%
155451  Nov 2011    780,292   142,302 (18.24%)   114,013   14.61%   80.12%
160036  Dec 2011    885,172   156,321 (17.66%)   120,631   13.63%   77.17%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
164780  Jan 2012    998,087   170,082 (17.04%)   136,985   13.72%   80.54%

166149  Feb 2012  1,037,382   174,584 (16.83%)    54,346    5.24%   31.13%

Edit: I just found these 100% pure allinvain coins - undiluted after 24 hops from when 25k BTC was stolen from his computer.
Edit 2: I don't mean to imply that the allinvain coins haven't been thoroughly looted.  They have touched 755,796 different addresses since being stolen and are currently sitting in 109,235 different addresses, including 8 from my own personal wallet.  The exact same 8 as have pizza coins in them, it turns out.

user132: Here is a possible schema describing transactions from two addresses A and B that contain initially 50 BTC each:
     (A) 50 btc --tx1-----------------------> 25 btc (C)
                   \
                    `-> 25 btc (D) --.
                                      \
                                       tx3--> 50 btc (*)
                                      /
                    .-> 25 btc (E) --'
                   /
     (B) 50 btc --tx2-----------------------> 25 btc (F)

There are three transactions here, and they mention only values: those transactions are stored in the block chain like:

tx1: (input on A: 50BTC; output on D: 25BTC, output on C: 25BTC)
tx2: (input on B: 50BTC; output on E: 25BTC, output on F: 25BTC)
tx3: (input on D: 25BTC,  input on E: 25BTC; output on *: 50BTC)

Only global amounts are involved, not individual satoshis. Could you tell where each of the satoshis in * came from? A or B? Just impossible.
Conclusion: There is no such thing as individual satoshis, they don't have identities in the Bitcoin framework.
(And it's the same, or even worse, for bitcoins. An individual bitcoin is not well defined. It might be a grouping of smaller amounts in the same place (wallet), or at the same address, or in the same transaction, but at a given point in time.)
It is however possible to track money flows between addresses, which may “dilute” into other flows, as illustrated in this answer.

22: <p>For example, if I wanted to "collect" important bitcoins is there any way to track a coin rather than a series of transactions? If I wanted one of the bitcoins from the infamous "<a href="http://bitcointalk.org/?topic=137.0">Bitcoin pizza</a>" purchase, for example, is there any way to do so?</p>

<p>Perhaps the question I <em>should</em> be asking is more like "Do bitcoins themselves even exist or just the records of transactions?"</p>
 1304: <p>You might want to have a look at the concepts of "taint" and "colored coins". You can start here:</p>

<p>Taint: <a href="https://bitcointalk.org/index.php?topic=92416.0" rel="nofollow">https://bitcointalk.org/index.php?topic=92416.0</a></p>

<p>Colored Coins: <a href="https://bitcointalk.org/index.php?topic=106373.0" rel="nofollow">https://bitcointalk.org/index.php?topic=106373.0</a></p>
 2157: <p>If you know the TX number, you can go to blockchain.info, search the TX number, click "View Tree Chart" and a tree chart will show up and you can click on the yellow/orange circles. That is how I found out a bitcoin I sent to an exchange ended up plying ping-pong with SatoshiDice.</p>
 85: <p>The simplest way to understand why the answer is "no" is to understand a very basic concept about Bitcoin transactions:</p>

<p>Each transaction (except generating transactions) has one or more "inputs" that pull in Bitcoins. And each transaction has one or more "outputs" that offer those Bitcoins.</p>

<p>In the transaction itself, all the Bitcoins pulled in form a pile. There is no way to track a particular input to a particular output, nor is that meaningful.</p>

<p>Imagine a transaction pulls in 25 Bitcoins from one place and 25 Bitcoins from another place and then sends out 10 Bitcoins to each of five different places. What does it mean to ask which input the coins in a particular output came from?</p>

<p>Bitcoins are more like account balances than pennies. If you put 10 pennies in a pile and give 1 out, you can ask which penny they got. But if you deposit two $10 checks and then withdraw $5, which check did that $5 come from? It's not even a meaningful question.</p>
 81: <p>This is actually similar to the <a href="https://bitcoin.stackexchange.com/questions/181/can-bitcoins-be-counterfeited">"Can a bitcoin be counterfeited?"</a> question.</p>

<p>The answer is no, because as you seemed to hint at, there is no such thing as a bitcoin. There is simply a transaction list, that has consensus around it, where no wallets are ever allowed to go negative.</p>
 659: <p>I've been playing with <a href="https://github.com/gavinandresen/bitcointools" rel="nofollow noreferrer">Gavin's "bitcointools"</a> (<a href="https://bitcoin.stackexchange.com/questions/2828/how-many-bitcoin-addresses-are-have-been-carrying-a-balance">again</a>) to track what happened to the famous "pizza" Bitcoins.</p>

<p>It turns out that rather than being rare collector's items, the <a href="https://bitcointalk.org/index.php?topic=137.msg1195#msg1195" rel="nofollow noreferrer">10,000 BTC</a> exchanged for <a href="http://heliacal.net/~solar/bitcoin/pizza/" rel="nofollow noreferrer">two pizzas</a> have spread out to over a million different Bitcoin addresses since buying the pizzas, not counting the dilute fragments that ended up in transaction fees.</p>

<p>As of block 166149, on Feb 10th 2012, 1,037,382 addresses have held the pizza coins since they were spent.  174,584 of those still hold pizza coins (the others may or may not be empty addresses, since it's possible to have two different transactions output to the same address without the coins becoming mixed together.  In other words it's possible to have "pizza coins" and "non pizza coins" in the same address and still be able to tell which are which.  Of the approximately 600k addresses which are currently holding funds, around 29% of them contain pizza coins.</p>

<p>The shortest chain of transactions from the pizza purchase to currently held pizza coins has length 9, and the longest has length 6,723.</p>

<p>There is no currently unredeemed output which contains 100% pure pizza coins.  All the pizza coins have been diluted somewhat with other coins.  The purest remaining are <a href="http://blockexplorer.com/t/A7RS7vqSx1" rel="nofollow noreferrer">these 100 BTC</a> which are 90.7276% pure pizza coin, and just 11 transactions separated from the pizza transaction.  (The most recent 9 transactions each only have 1 input, so it's easy to follow it back that far.  In the next transaction back the pizza coins came from both the last but one input, worth 4223 BTC, and 5th from last input, worth 5777.  Together those 2 inputs make up the full 100% pure 10k BTC pizza coins.  The other inputs in this big transaction, worth 1022 BTC in total are the only non pizza coins introduced.  10000 * 100 / 11022 = 90.7276%, the purity). </p>

<p>I also checked my wallet to see if I was holding any pizza coins.  8 of my addresses are holding pizza coins, but very diluted.  My 'strongest' has a purity of 1.1760%, and is a <a href="http://blockexplorer.com/t/6cfKNoE1UR#o0" rel="nofollow noreferrer">tiny withdrawal</a> I made from MtGox in October 2011.</p>

<p>Finally, here's some data showing the month-by-month spread of the pizza coins:</p>

<pre><code>pizza payment of 10000.00000000 BTC to 17SkEw2md5avVNyYgj6RiXuQKNwkXaxFyQ
is in block 57043

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
 58815  May 2010          4         2 (50.00%)         4  100.00%  200.00%
 63561  Jun 2010          4         2 (50.00%)         0    0.00%    0.00%
 71436  Jul 2010         26         8 (30.77%)        24   92.31%  300.00%
 77452  Aug 2010         34        10 (29.41%)        13   38.24%  130.00%
 82997  Sep 2010        138        37 (26.81%)       106   76.81%  286.49%
 88892  Oct 2010      2,016       265 (13.14%)     1,898   94.15%  716.23%
 94801  Nov 2010      6,295       577 ( 9.17%)     4,428   70.34%  767.42%
100409  Dec 2010      7,510       835 (11.12%)     1,464   19.49%  175.33%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
105570  Jan 2011     13,271     1,540 (11.60%)     6,150   46.34%  399.35%
111136  Feb 2011     19,055     2,632 (13.81%)     6,423   33.71%  244.03%
116038  Mar 2011     42,027     5,605 (13.34%)    24,341   57.92%  434.27%
121126  Apr 2011     69,544     9,085 (13.06%)    29,727   42.75%  327.21%
127865  May 2011    123,997    26,032 (20.99%)    57,911   46.70%  222.46%
134121  Jun 2011    249,138    54,047 (21.69%)   132,348   53.12%  244.88%
139035  Jul 2011    382,845    93,928 (24.53%)   146,156   38.18%  155.60%
143408  Aug 2011    494,140   108,340 (21.92%)   126,134   25.53%  116.42%
147565  Sep 2011    589,942   119,491 (20.25%)   111,178   18.85%   93.04%
151314  Oct 2011    680,787   131,370 (19.30%)   105,320   15.47%   80.17%
155451  Nov 2011    780,292   142,302 (18.24%)   114,013   14.61%   80.12%
160036  Dec 2011    885,172   156,321 (17.66%)   120,631   13.63%   77.17%

-block  --date--  --total--   ---used--%total-   -active---%total---%used-
164780  Jan 2012    998,087   170,082 (17.04%)   136,985   13.72%   80.54%

166149  Feb 2012  1,037,382   174,584 (16.83%)    54,346    5.24%   31.13%
</code></pre>

<p>Edit: I just found these <a href="http://blockexplorer.com/t/69fDjp12gB#o0" rel="nofollow noreferrer">100% pure allinvain coins</a> - undiluted after 24 hops from when 25k BTC was <a href="https://bitcointalk.org/index.php?topic=16457.msg214423#msg214423" rel="nofollow noreferrer">stolen from his computer</a>.</p>

<p>Edit 2: I don't mean to imply that the allinvain coins haven't been thoroughly looted.  They have touched 755,796 different addresses since being stolen and are currently sitting in 109,235 different addresses, including 8 from my own personal wallet.  The exact same 8 as have pizza coins in them, it turns out.</p>
 132: <p>Here is a possible schema describing transactions from two addresses <code>A</code> and <code>B</code> that contain initially 50 BTC each:</p>
<pre><code>     (A) 50 btc --tx1-----------------------&gt; 25 btc (C)
                   \
                    `-&gt; 25 btc (D) --.
                                      \
                                       tx3--&gt; 50 btc (*)
                                      /
                    .-&gt; 25 btc (E) --'
                   /
     (B) 50 btc --tx2-----------------------&gt; 25 btc (F)
</code></pre>
<p>There are three transactions here, and they mention only values: those transactions are stored in the block chain like:</p>
<ul>
<li><code>tx1</code>: <code>(input on A: 50BTC; output on D: 25BTC, output on C: 25BTC)</code></li>
<li><code>tx2</code>: <code>(input on B: 50BTC; output on E: 25BTC, output on F: 25BTC)</code></li>
<li><code>tx3</code>: <code>(input on D: 25BTC,  input on E: 25BTC; output on *: 50BTC)</code></li>
</ul>
<p>Only global amounts are involved, not individual <em>satoshis</em>. Could you tell where each of the <em>satoshis</em> in <code>*</code> came from? <code>A</code> or <code>B</code>? Just impossible.</p>
<p><strong>Conclusion:</strong> There is no such thing as individual <em>satoshis</em>, they don't have identities in the Bitcoin framework.</p>
<p>(And it's the same, or even worse, for <em>bitcoins</em>. An individual <em>bitcoin</em> is not well defined. It might be a grouping of smaller amounts in the same place (wallet), or at the same address, or in the same transaction, but <strong>at a given point in time</strong>.)</p>
<p>It is however possible to track money flows between addresses, which may “dilute” into other flows, as illustrated <a href="https://bitcoin.stackexchange.com/a/2900/132">in this answer</a>.</p>
