CUBE
Metal Gear Solid: Twin Snakes (not really an exclusive as such)
Metroid Prime
Mario Sunshine (as a Players Choice title it is well worth a go)
Zelda: Wind Waker
F-Zero: GX
Viewtiful Joe
Animal Crossing 1/2 (maybe? unsure)
Resident Evil + Zero + 4
Eternal Darkness
Super Smash Bros (not to all tastes (inc me) but many love it)
Waverace: Blue Storm
Pikmin 1/2
Super Monkey Ball 1/2
Skies of Arcadia Legends (also on DC)
Ikaruga (also on DC)
Star Wars Rogue Squadron II (or maybe III for the co-op levels)
Mario Kart: Double Dash
1080 Avalanche
Wario World
Lost Kingdoms 1/2
Tales of Symphonia
Baten Kaitos
All *exclusive* (unless noted), all top-notch. Others that never made the list (mainly as they are much more 'marmite' in nature!) are P.N.03, Cubivore, Mario Party, Gotcha Force, Megaman Network Transmission......
Hope that helps in some way.