Paper Mario: The Thousand Year Door
is by far my favorite Gamecube game. I love, love, LOVE this game. Not only is it visually beautiful, but the story is great, the controls are great, and the gameplay is just so much fun and just the perfect amount of difficulty.
The Simpsons: Hit and Run
is also a fun game to have around. It really is a Simpsons-themed Grand Theft Auto. It's something you can play a little here and there without having to set a lot of time aside for it. Super Smash Bros. Melee
is another game like this, and one that is especially fun when playing with a group of people.
I know I've played Eternal Darkness
but I must not have thought it was that awesome, because I can't seem to remember anything about it.
I played the Lego Star Wars
games on the Gamecube and really enjoyed them. I also liked Star Fox Adventures
Finally, I would suggest picking up a copy of Luigi's Mansion
if you can find it for cheap. You probably can because I believe it was bundled with the console for a while. It is a Mario type adventure game that stars, obviously, Luigi instead. He travels through a haunted mansion using his vacuum to suck up ghosts. It's a strange but fun take on that type of game.