The PS 1 has a huge library of games from all genres. I've played a lot of great games and here are the ones that stood out:
Tenchu: Stealth Assassins - an awesome game that made you feel like an actual ninja. You could set traps, slit throats, throw shurikens, and even feed your foes poisoned rice.
Metal Gear Solid - another stealth game with an amazing story about war and nanomachines (whatever that is). Aside from the story, MGS also featured lots of weapons and gadgets at your disposal and epic boss battles.
Final Fantasy 7-9 - whenever I played a FF game in the past, I was always filled with joy. Even if they had mediocre stories, the games were still interesting because of the abundance of things to do.
Tekken 3 - my favorite fighting game on the system. It was an almost perfect port of the excellent arcade game by Namco plus a lot of different extras thrown in.
Xenogears - another RPG from square which deviated from the traditional turn based formula to an action turn based fighting system hybrid. The thing that sets this apart from the rest though is its incredible story. This game is epic and I still remember it fondly up to this day.
And the winner is: Xenogears!