1. Star Wars Rogue Squadron 2 - Rogue leader. Not just my favorite Gamecube game, but my favorite game from the whole generation. Gorgeous for the time with several of the levels like the Death Star and Hoth still looking good today, nearly 20 years later. Short but with incredible replay value.
2. Smash Bros. Melee. The reason I got a Gamecube. Even if I prefer some of the later games in the serie, Melee was something truly special and my introduction o many Nintendo franchises.
3. Wind Waker. Not my favorite 3D Zelda and the pacing in the last few hours is horrible, but overall a very fun and charming game.
4-5 Metroid Prime and Resident Evil 4. 2 Great games I only really got into on the Wii because of that system's amazing pointer controls.
Beyond that it's hard to rank. At the time I was more into games from familiar properties like Two Towers, Batman Begins, or Ultimate Spider-Man.