I'd have flipped Eternal Darkness and RE4. Eternal Darkness was creative and unique, but the gameplay really hasn't aged well, while RE4 is still just as good today as when it released.
In no particular order:
-Tales of Symphonia
-Super Smash Bros. Melee
-Phantasy Star Online
-Mario Kart: Double Dash
-Super Mario Strikers (Only with 4 players)
-TimeSplitters 2 and 3
-Conflict: Desert Storm
To me, the Gamecube will always be the multiplayer-console, as I never owned the console myself, but we used to play it at my friends house all the time, so any game with a proper local multiplayer was always in rotation.
No Guitar Hero for Gamecube.
Oh, that's right. I mixed up the Wii versions there.