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.