user11867: I run Bitcoin-Qt and Bitcoin Armory on a laptop. I don't have the space to store the whole 20 GB (or however big it is now) blockchain.
I understand the need to run through the entire thing for security, but I'd like it to only store relatively recent blocks + the summarized version (for example, the database of unused outputs / computed ledger). I'd like good security; I just don't have the space to store the whole thing.
Is there some way to configure Bitcoin-Qt / bitcoind to trim its data to a more reasonable size after it's gone through and processed the chain?

user5651: This answer is now outdated please see Answer below

At this time, no, you can not strip the block chain (as far as I
  know). There is one programmer (Mark Freidenbach AKA maaku) who is
  working on further compressing the blockchain for the Satoshi bitcoin
  clients.
The entire block chain is currently needed to verify all coins are
  legitimate from the beginning of time. Plus there are coins in the
  older blocks that would not be included in new blocks, so some old
  miners might lose their coins.
1: https://en.bitcoin.it/wiki/Original_Bitcoin_client


user3697: Since Bitcoin-Core 0.11.0 you can prune (trim) the blockchain in Bitcoin-Qt.
But not from the UI.
You need to add prune=550 to your bitcoin.conf file and restart Bitcoin-Qt.
Explanation:
-prune=<target in MiB> will tell bitcoin-core to remove blocks which are older than oldest block that can be kept with a chainsize (sum of block-sizes) of <target> (min. 550MiB as example above shows). A minimum of 550MiB ensures to keep at least 288 blocks (~2 days). 
(simple explanation not including undo-data)
Restriction:
-prune does disable all wallet functions in version 0.11 (will work with a wallet in version 0.12).

11867: <p>I run <a href="https://en.bitcoin.it/wiki/Bitcoin-Qt">Bitcoin-Qt</a> and <a href="https://bitcoinarmory.com/">Bitcoin Armory</a> on a laptop. I don't have the space to store the whole 20&nbsp;GB (or however big it is now) blockchain.</p>

<p>I understand the need to run through the entire thing for security, but I'd like it to only store relatively recent blocks + the summarized version (for example, the database of unused outputs / computed ledger). I'd like good security; I just don't have the space to store the whole thing.</p>

<p>Is there some way to configure Bitcoin-Qt / bitcoind to trim its data to a more reasonable size after it's gone through and processed the chain?</p>
 5651: <p>This answer is now outdated please see <a href="https://bitcoin.stackexchange.com/a/38847/5651">Answer below</a></p>

<blockquote>
  <p>At this time, no, you can not strip the block chain (as far as I
  know). There is one programmer (Mark Freidenbach AKA maaku) who is
  working on further compressing the blockchain for the <a href="https://bitcoin.stackexchange.com/a/38847/5651">Satoshi bitcoin
  clients</a>.</p>
  
  <p>The entire block chain is currently needed to verify all coins are
  legitimate from the beginning of time. Plus there are coins in the
  older blocks that would not be included in new blocks, so some old
  miners might lose their coins.</p>
  
  <p><a href="https://bitcoin.stackexchange.com/a/38847/5651">1</a>: <a href="https://en.bitcoin.it/wiki/Original_Bitcoin_client" rel="nofollow noreferrer">https://en.bitcoin.it/wiki/Original_Bitcoin_client</a></p>
</blockquote>
 3697: <p>Since Bitcoin-Core 0.11.0 you can prune (trim) the blockchain in Bitcoin-Qt.
But not from the UI.
You need to add <code>prune=550</code> to your bitcoin.conf file and restart Bitcoin-Qt.</p>

<p><strong>Explanation:</strong>
<code>-prune=&lt;target in MiB&gt;</code> will tell bitcoin-core to remove blocks which are older than oldest block that can be kept with a chainsize (sum of block-sizes) of <code>&lt;target&gt;</code> (min. 550MiB as example above shows). A minimum of 550MiB ensures to keep at least 288 blocks (~2 days). 
<em>(simple explanation not including undo-data)</em></p>

<p><strong>Restriction:</strong>
<code>-prune</code> does disable all wallet functions in version 0.11 (will work with a wallet in version 0.12).</p>
