I would like to throw in a game that you will probably never get your hands on, but it's the game that made me get a GameCube. As in, I bought it before I actually owned the system.
The Legend of Zelda: Collector's Edition.
Some poor soul traded this in to a local GameStop and I saw it on the shelf for thirty five bucks. Snatched that right up. Comes with the original Legend of Zelda, Zelda II, Ocarina of Time, and Majora's Mask. If you can someone find this game (and not pay out the nose for it), it is worth it.
No one's mentioned Resident Evil 4 yet? Really? I see that Resident Evil in general is mentioned, but 4 needs to be here too--unless you have another version with the extras.
The remake of Metal Gear Solid. Better graphics and controls, but still same acting and story.
Metroid Prime game. Or is there more than one on the system? Anyway, if you find them, grab them.
Fire Emblem, as others have said.
Twilight Princess because this was the game that I had planned on getting my system for, until I lucked out with Collector's Edition
Rogue Squadron II and III. II is probably the closest we've gotten to true Star Wars space combat on consoles, period.
Tales of Symphonia, if you can find it.
SSB Melee, if you have friends to play with. Good solid party game, so long as there's not that one person who can stomp everyone else.
Unfortunately, with the GameCube now two generations old, games for it are going to be hard to find. The good games, many of which I and others have listed, are going to be even harder to find, and they probably won't be cheap. But if you can find them, they are worth it. The GameCube didn't have as big a library of stellar games as the other two, but the gems it did have make it worth it if you can find some of them.
