I thought it'd be fun, Cronos started this at EmuChrist, but there wasn't much going on with it, so I thought I'd add some comments!
This isn't exactly in order, but are 10 games I like on the Gamecube, there are others I like, but this is the top ten!
#10 Super Monkey Ball $19.99 3rd party
Marble Madness with simians, it has some crazy levels and some nice bonus games, it'll keep you occupied for a while.
#09 Super Mario Sunshine $16.29
Mario 64 with a water gun and a more open environment. It's a bit harder than Mario 64 and the controls and camera can get wonky, but it's fun.
#08 Geist $8.00 3rd party
A unique and fun to play 3rd party FPS, it's amazing this landed on the Gamecube and not the XBOX. Thanks for telling me about this game Cronos.
#07 Metroid Prime $19.99
More FPS goodness and the 1st 3D Metroid, it would lead to 2 more great sequels.
#06 Mario Kart Double Dash $16.00
A unique Mario Kart where 2 players can share the same racing car. It's fun if you don't play 150cc.
#05 Eternal Darkness $11.79 3rd party
A dark game with a mature rating that fucks with you, has replayability, and it came out for the 'Cube? WOW!
#04 Gauntlet Legends 3rd party
Warrior needs food badly! an excellent port of the arcade game, great 4 player fun.
#03 The Legend of Zelda WW with OoT/MQ $FREE
This was the reward for buying a Gamecube at a Wal Mart at the Right time. Even near the end of the 'Cube's lide this would have been well worth $50 if you purchased a $99 Gamecube. In fact buying the Zelda's alone if around $45 USED now @ $16 for WW and $26 for the Oot/MQ.
#02 Ikaruga $10.00 3rd party
The best shooter on the Gamecube, because it seriously lacks shooters. Unless you want to shell out $70-$100+ on the Dreamcast, you'll want the Gamecube version, which can often be had ~ $30.
#01 Tales of Symphonia 3rd party $16.29
A 3rd party RPG, the likes which you won't see on the Gamecube, Nintendo went out of their way to get this gem of a game. It rocks.
There Cronos, 6 3rd party games vs 4 Nintendo games, so there are a few great 3rd party games for the Gamecube!
The prices I listed are what I paid for them... Yeah, I'm a cheap bastard!