A sampling of PS2 exclusive games from my collection, including:

TimeSplitters
Blood Will Tell
RAD – Robot Alchemic Drive
24: The Game
SOCOM 1 & II
AirBlade
Aqua Teen Hunger Force Zombie Ninja Pro-Am
Champions of Norrath
Front Mission 4 & 5
Guilty Gear X2
Destruction Derby Arenas
Gungrave
Katamari Damacy
Okage: Shadow King
War of the Monsters
Downhilll Domination
Rogue Galaxy
Shadow Hearts: Covenant
SSX
Suikoden IV
TimeSplitters
Xenosaga Episode I
Xenosaga Episode II
Xenosaga Episode III