I've been going to blockchain.info frequently to check addresses, transactions, blocks, etc. But since I've already got the blockchain on my hard drive, this seems kind of pointless. Is there any software similar to blockchain.info that runs natively on Linux, and uses Bitcoin-qt/bitcoind's blockchain, and therefore doesn't require an internet connection?
Abe does exactly what you want. I will walk the entire blockchain from bitcoin-qt/bitcoind and populate a local database. It supports several database backends including sqlite, Postgres, MySQL and Oracle.
It will take quite some time to walk the blockchain and populate the database, possibly a few days.
Unfortunately, there is no good (easy to use, desktop software) program for this. You can use Bitcoin-Qt's debug window (or JSON-RPC server, if you choose to enable it) to request information using methods like getblock/getrawtransaction, but it isn't very user-friendly.
Well, I don't think what you are looking for does exist.
You need to know that bitcoind only keeps your data in binary format. When it receives and stores blocks, it will check for transactions involving addresses in your wallet. All the other ones are just written to the disk. Since this data is binary, it is extremely slow to search through it.
Programs that allow you to look up every transaction and block have a more complex data structure with many indexes meaning greater storage volume.
As Meni and Joe mention in the comments, Abe seems to be something that can help you, though it will need additional disc space.
Another Block Explorer implementation that I know of, is the one from the BitcoinJS team that is written in Node.js. It can be found on GitHub.