I think my favorite game on the Playstation platform is Final Fantasy X, which is actually a PS2 game. It's the best Final Fantasy game I've ever played and probably still the best role-play game I've ever played, even over Skyrim. I wish they would come out with a remake of Final Fantasy X for PS3 and/or Xbox 360, with the only difference being better graphics.
Amanda - I'm with you about Final Fantasy X; it's definitely the best Final Fantasy!
As for me, my favorite Playstation game, between all 3 Playstation platforms, is the Grand Theft Auto series. Of all the Grand Theft Autos, Vice City is my favorite, but GTA is just about the only series I've come across where I actually like ALL the games in the series, although I'll admit I do like some of them better than others.