Nintendo has confirmed that the Wii console will support both the original Gamecube controller and the wireless Wavebird for all Gamecube titles and some Wii games.
Nintendojo recently reported that the Wavebird and regular controllers will work for the Nintendo Wii. The Escapist has independently confirmed that this is indeed the case, the Wavebird will work just fine with the new system. Primarily for Gamecube games, Nintendo has said the old controllers may also be enabled some Wii titles as well, but they did not specify which ones.
Gamecube owners should note that the Wavebirds will still need the receivers that plug into the console to work.