Spyro 1-3
Crash Bandicoot 1 and 3 (didn't find anything new in 2 myself, it was very similar to 1, in my opinion, but some people like it so play it if you like Crash 1 I guess.)
Ape Escape; an all around fun game, I think its aged well and I love its soundtrack.
Croc: Legend of the Gobbos (if you can find it, I haven't seen it around in awhile, I'm glad I still have my copy.)
Tomba/Tombi (if you can't afford/find the ps1 version its pretty cheap off the PSN, and really worth playing.
Medievil, wasn't GREAT for me but still good and worth playing.
if you were a Digimon kid; Digimon World (not for everyone but if you like that sort of thing its enjoyable.)
Rayman 2, I never played the first so I can't say about that one, but Rayman 2 is fun, fairly challenging (or at least it was last time I played) and has an interesting varied world.
Legends of Legaia has a massive world and a pretty good story, it falls a little flat at the end but this is still one of my top 5 ps1 games.
Jade Cocoon is again not for everyone. Just a warning though the beginning of the game is basically all talking and pretty long.
Kula World/Roll Away, which is trippy as hell and really fun to play. This is also on PSN from memory. I think original copies are pretty expensive now.
These are all the ones I still own and play on my ancient PAL ps1 (its right from when they were first made and still runs better than my ps3 haha), some may not be your sort of thing but each to their own.