It's incredible how ps1 games aged terribly, SNES games in general are much more enjoyable for today's standards than ps1. And ironically enough the games on ps1 that aged better are mostly the 2d ones and the 3d ones that focused more on different art style instead of realism . Anyway, let's list some ps1 games that are still worth our precious time. 

Castlevania: symphony of the night. 

FF IX

Crash Bandicoot 3.

Rayman

Megaman X series

Personally:
- FFVII-FFIX
- Dino Crisis 1-2
- Street Fighter Alpha 3
- X-Men vs SF/Marvel vs Capcom
- Resident Evil 1-3

One Piece Mansion
Devil Dice

Going just by how well the graphics hold up. Story and gameplay-wise I could list a lot more.

Final Fantasy IX (Some of the best visual design I've ever seen in any game to date)

Suikoden 1 and 2 (They went with sprites instead of 3D models, so they've aged much better than most other games of the era)

Crash 3 (Even back then Naughty Dog was really good at using every last bit of power the console had to offer)

In general games that stuck with 2D hold up very well.

Persona
Persona 2 - (part1) Innocent sin (fan patched if you want ps1 version)
Persona 2 - (part2) Eternal Punishment
Final Fantasy 4 up to 9
Chrono Trigger (even if snes version loads better)
Chrono Cross
Alundra 1 & 2
Breath of fire 3 & 4
Thusand Arms
Wild Arms 1,2
Lunar I & II

This would probably be a good time for me to take notes, as I passed the PS1 generation.

I went through a bing of collecting some classics a while back, got a good haul.

Obviously the FF games. Vagrant Story. Crash series (including racing), any Capcom fighter. Tekken 3. Devil Dice, Kurushi (plus Final). WipeOut series. Discworld (if you can get your hands on it). Toy Story 2, the game (it's really good). Twisted Metal World Tour.

Sure there are more.

Metal Gear Solid, still probably my favorite game of all time.

Assault Rigs