Chrono Trigger: First RPG I ever played, and still one of the greatest games of all time.
Final Fantasy IV: Amazing story, great soundtrack, and my favorite cast of characters of the series.
Breath of Fire II: My favorite BoF.
Super Mario RPG: Still the best Mario RPG ever made.
Final Fantasy VII: Probably the best RPG on PS1.
Final Fantasy IX: The first one I played on PS1, still a great game.