Animal Crossing
Battalion Wars
Beyond Good & Evil
Eternal Darkness: Sanity's Requiem
F-Zero GX
Fire Emblem: Path of Radiance
Ikaruga
Killer 7
The Legend of Zelda: Wind Waker
Metroid Prime
Metroid Prime 2 Echoes
Metal Gear Solid: Thw Twin Snakes
Paper Mario: The Thousand-Year Door
Pikmin 2
Prince of Persia: The Sands of Time
Resident Evil 4
Soulcalibur II
Super Mario Sunshine
Super Smash Bros. Melee
Viewtiful Joe

Omitting Resident Evil from the list, that would be my 20 must-haves for the system. I've played all extensively, and beaten all but 2 of these games, and they're a mandatory purchase as far as I'm concerned.