blkindex.dat are Berkeley Database files. They can be read using standard tools, but aren't human readable by themselves.
blk0001.dat (and additional blk000n.dat blocks) contain the blockchain itself, that's just a binary concatenation of the blocks.
wallet.dat contains your private keys, your address book, a copy of the transactions that send coins from or to one of your addresses, accounts, reserve keys, personal settings, and a pointer to the current best block.
addr.dat contains IP addresses of peers, both those you've connected to yourself or those you've only heard about. It has been replaced by peers.dat since 0.7.0
peers.dat contains the same information as addr.dat, but using an efficient custom format.
blkindex.dat contains an index of the blocks and transactions that can be found in all the
I don't know about any standalone tools that convert
blkindex.dat to human-readable form, although blockexplorer.com can be used to inspect the blockchain, and
addr.dat just contains IP addresses.
Update: the data above is only valid before v0.8.0. As of v0.8.0, a new database structure (with associated filesystem layout) is used for blocks and indexes.