My list of recommendations:
Non-Exclusives:
Capcom VS. SNK 2
Soul Calibur 2
Prince of Persia: The Sands of Time
Resident Evil 4
Tales of Symphonia
Exclusives:
Adventure
Metroid Prime 1
Legend of Zelda: Twilight Princess
Legend of Zelda: Wind Waker
Legend of Zelda: Four Swords Adventures
Fighting
Super Smash Bros. Melee
Platforming
Super Mario Sunshine *Mute when cut-scenes start, trust me.*
RPG
Baten Kaitos
The other Baten Kaitos
That's all I can think of off the top of my head.