PS1: Got the console with Duke Nukem: Land of the babes and bought GT2 right after that.
PS2: GTA: Vice City Stories/Burnout Dominator.
PS3: Gran Turismo 5 bundled with the console, then bought GTA IV.
PSP: Gran Turismo (bundled with the console) and GTA:VCS (yeah again.)
My very first PS3 game. Journey. Followed by Sonic Generations. There's a lot of good games on PS3 I never got to explore due to owning an Xbox 360. But I now have the time to sit back and play them.