Can Bitcoin-Qt be configured to trim the blockchain? I run Bitcoin-Qt and Bitcoin Armory on a laptop. I don't have the space to store the whole 20&nbsp;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?
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=&lt;target in MiB&gt; 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 &lt;target&gt; (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).