Saga Frotnier II has always been one of my favorites, never understood the hate, both are unique titles with long lists of pros and cons.
Here's a fairly long list of games I'd recommend, PS1 was a big hit with me "back in the day".
Alunda (zelda like game, pretty difficult)
Azure Dreams (fun roguelike-esque game)
Brave Fencer Musashi
Breath of Fire III & IV (personal favorites)
Brigandine (SRPG)
Grandia (simplistic but endearing)
Jade Cocoon
King's Field series (including Shadow Tower)
Legend of Mana (deviously complex, don't let the cutesy graphics turn you away)
Medieval I & 2
Megaman Legends 1 & 2
Monster Rancher 2 (I've sunk more time into this game than I care to admit)
Parasite Eve 1 & 2 (first is a altoghether decent jrpg, second is like resident evil with rpg elements, scary as shit at times too)
Persona 2 (you can now play both "episodes" of this game, both are good)
Sheep Raider (like metal gear solid, only you play as Wile E. Coyote)
Soul Reaver
Spyro series
Star Ocean 2
Tales of Destiny & Phantasia (the tales series is hit or miss as a whole)
Tenchu games
Tomba games
Vandal Hearts games (srpg, they kind of suck, no reason not to check them out through emulation though)
Vanguard Bandits (same as above)
Wild Arms games
Valkyrie Profile (damn good game)
Vagrant Story (a must play title)
Xenogears (fuck can't believe I almost forgot this game, best jrpg ever made imo)
Edit: Didn't mention FFT or Tactics Ogre because both games have superior remakes on the PSP, still worth emulating if you don't own a PSP, I enjoy Tactics Ogre more myself. Final Fantasy series is obligatory and overated, FFIX is probobly the best on the PS1. Koudelka kind of sucks, but the Shadow Hearts games on the PS2, which are sort of sequals, do not.