Derrdumdumdum...beerrdarrrr....Derrdumdumdum...beerrdarrrr..Goldeneeeyyyyeee. Oh wait, already been done.
I would say either MGS, Crash bandicoot 2/3 or Mario 64.
Metal Gear Solid because it took game to a point no-one had even tried, never mind succeeded so spectacularly. Ironically the limits of the PS1 probably made it better, with roughly 1.4gb to play with Kojima had to be quite succinct.
Crash Bandicoot because no games before or after have been so funny, family friendly and playable. Whilst CB2 is insanely difficult, it was also fair, you died because you missed. not because of a glitch.
Mario 64 because it was the first 3-D platformer I've ever played, I also got my hands on it again last year and discovered that patformers haven't really changed at all in the last 11 years. It's also one of the best designed platformers ever made. Mario has an enormous array of moves in an era when move-jump-attack was more than most platformers could muster.
The levels were designed so that you had to use all of them, but without the lead by the hand sign posting that seems to permeate all games nowadays.
Although if you forced me to pick one game it would be Colony Wars: Vengeance
That game was gorgeous, it still looks good now even on the PS1. Insanely difficult and at times hopelessly unfair. All it's faults are forgiven though for one simple reason, the sound.
Full surround sound on the PS1 and the only game to ever blow out my TV's speakers, loudest explosions in any game ever.
fzzt......BOOOOOOOM!!!