Here is a list of my favorite PS1 games.

Metal Gear Solid (probably the best & most atmospheric game on the PS1)

Resident Evil 1-2

Gran Turismo 1-2

Tekken 1-3

Final Fantasy 7-9

Tomb Raider

Command and Conquer Red Alert: Retaliation (was fun systemlink)

Crash Bandicoot 1-3

Diablo

Tony Hawk's Pro Skater 1-3