I hacked my brother's Wii this weekend. It
was fairly painless (and pointless at present). All you need is a copy
Zelda: Twilight Princess
(which I don't have, hence using my brother's Wii for this) and an SD
card. You use the
Twilight Hack as a
Zelda saved game, which then causes a buffer overrun when you try to
talk to the first character in the game. This is exploited to load a
boot loader which loads and runs a
boot.elf file off an SD card in
the Wii's memory card slot. Pretty easy to do.
There's not a lot out there at present. Wiibrew seems to be the main hub of activity. I tried the GameCube Linux Proof of Concept Linux port; once they add USB support it might actually be useful as that'll open up mass storage and input via a keyboard. There's a Sega Genesis emulator on Wiibrew which isn't too bad, but I found it a bit temperamental at reading ROM images.
Still, it's a start and it's pretty nifty that you can do this without having to modify your Wii in any way. I expect more groovy homebrew will appear as the hardware of the Wii gets better mapped out.