I believe that my first PS2 game was Vice City. Got it just after it came out, and it was one of the best days of my young gaming life. Holy crap was I pumped for that game, didn't let me down either. Shortly afterwards I got 007 Nightfire. I played those games to death.
I've never owned a PS1 or PS3. Not really much of a console person. But man did the PS2 have some fun ass games.