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.
Gladius is another one I've heard good things about but need to try.
Retro Tech Select - My Youtube channel. Covers throwback consumer electronics with a focus on "vid'ya games."