I'm not sure I have a favorite game on the Playstation. There were a lot of games which I really liked for different aspects. For example, Chrono Cross and Final Fantasy 8 for the artwork and music, but not so much for the gameplay. Oddworld for the gameplay and how innovative it was. A few others, more for nostalgia than for their merits. There isn't a clear favorite for me, though. =]
This thread seems even more appropriate now, given that it's the PlayStation's 20th birthday this year. There are so many to chose from, but I think I'll go for the original Tomb Raider. That was the game that blew me away at the time. A close second is Resident Evil.