I'm not going to list the games that everyone else already listed in this thread. Now that I got that out of the way.
Def Jam Fight For NY(Mostly if you like seeing some funny finishers or if you're a fan of rap.)
Star Fox Adventures.
Star Fox Assault.(ONLY for multiplayer)
Sonic Adventure Battle 2 =).
Soul Calibur 2.
Metroid Prime 1/2.
DK Jungle Beat (if you can manage to find the bongos)
Billy Hatcher (one of sega's really GOOD, unique games, and only ever on gamecube. DOH!
Killer7(also on ps2)
Pac-Man VS (if you've got some friends, extra controllers and a GBA)
Pikmin for the gamecube is better than the wii version with motion controlls. Also mario sunshine, starwars rouge squadron rouge leader, super monkey ball and ssx tricky are some games I have had lots of fun with.
Incredible Hulk: Ultimate Destruction
Ultimate Spider Man
Die Hard Vendetta
Viewtiful Joe 1 & 2
Beyond Good & Evil
TimeSplitters 2 & 3
Paper Mario: The Thousand-Year Door
Def Jam Vendetta
Baten Kaitos 1 & 2
Fire Emblem: Path of Radiance
Sphinx and the Cursed Mummy
Peter Jackson's King Kong
Rayman 3: Hoodlum Havoc
There are just so many, this was a great time for gaming and the 3rd parties blessed the GC with so many titles. Had the Wii been near about on the same level in hardware then it'll be the same what with cross platform development and all that.
All of the "New Play Control" titles are better on the GC, they fucked up the controls on the games with exception to Donkey Kong Jungle Beat.