Resident Evil 4, without a doubt. It's one of THE best games I have ever played, in fact, it's my second favorite game ever. (First being The Legend of Zelda: Ocarina of Time!) Plus, this is coming from someone who never really preffered the Resident Evil series *isshot*. XD A true testament to the game's brilliance. Sure it IS on the PS2, but it was desigend originally for the Gamecube, and I prefer that version of the game.
However, if we are reffering to Gamecube ONLY games... I'd say... ANIMAL CROSSING!!!
XD Seriously, I loved that game when it came out and still play it to this day. Second would be Super Smash Bros. Melee, which holds up and continues to be a fun game to this day. Third... The Legend of Zelda: The Wind Waker. The graphical style in the game is amazing, as well as the gameplay. Classic Zelda stuff. But what Nintendo did SO right with the graphics, is give the world a real breath of life, they turned it into more than just Cel-Shading....
Ok... I'm done raving... XD