I'm not going to repeat what everyone else has said again and again, but I'll add some noteworthy games.
Gunners Heaven (not near Gunstar Heroes, but a good early PSX game)
Phalanx (yeah, it was out for SNES, but the PSX version had nicer music. Was a slight upgrade. I wasn't a big fan of PSX back then, but I ended up playing this game a decent amount for the music. Ah, and I don't know if this counts, as it was a hidden game in Zero Divide.)
Project: Horned Owl (used Masumune Shirow character/robot designs. I played it because it reminded me of the arcade games Steel Gunner 1 and 2, which I loved.)
Hermie Hopperhead (not the best platformer, but decent for the time)
I didn't really like Playstation back then though. I don't think the early games were that good, to this day. It's totally understandable though. 3D was brand new. Most of the developers were just trying to figure it out. And the 2D stuff didn't really have anything new. Just prettier graphics. There were many gems to come in 2 or 3 years after launch though.