Nothing to really add since everyone else listed the main games. But I'd also add Ridge Racer, Wipeout, and Toshinden into that pile. You can't underestimate the impact those games had for PS1's early successes. Ridge Racer was basically the perfect graphical showcase at launch. Toshinden out-flashed Virtua Fighter. Wipeout defined the coolness and style PS1 would become associated with in gaming.
However a lot of my personal favorites have ended up being smaller, more niche games, particularly those that have finally gotten English translations. Tomba 1 & 2, Klonoa, UmJammer Lammy, Ridge Racer 4, Galerians etc. They aren't the popular picks but they're some of my faves. And oddities like Planet Laika join them.