There are plenty of great PS1 games. These are my personal favorites.
Dino Crisis 2 - The gameplay could be quite dated to today's standards, but this was the first game that Capcom tried to make a fully action game out of a former survival horror game. This could be very well the spiritual precursor of Onimusha and Devil May Cry and, eventually, Resident Evil 4. Also, what's not to love about killing dozens of dinosaurs with huge weapons?.
Castlevania - Symphony of The Night - Not much to say here, just play it.
Vagrant Story - Amazing Action RPG with a wierd turn based hack n' slash system. Also, you get to fight bosses every 15 minutes.
Crash Bandicoot 2 & 3 - These were easily some of the best 3D platformers the PS1 offered. If you had to pick between 2 & 3, I'd go with 2. Just avoid the first one like the bubonic plague.
Spyro 2 - Another amazing platformer. If you can grab the whole trilogy, then good for you.
MediEvil - A rather bizzarre hack n' slash game with a touch of an Action/Adventure game and one of my favorite PS1 games. I easily finished this game like 4 o 5 times with 100% completition... it's that good.
Metal Gear Solid - 'Nuff said.
Mega Man X series - It's Mega Man, there's not much to say, other than these were some of the best 2D graphics the PS1 had to offer and they still hold up pretty well today. I'd go for X4, but if you can get 'em all, the better.
Resident Evil 2 & 3 - THE survival horrors of the PS1. 2 is my personal favorite, but 3 is still amazing. I don't like the first one, except for the GameCube remake, but if you're curious, get it too. Also, what's not to love about Jill sandwiches?
