Some of my favorites...
Vagrant Story: Incredibly complex but well-designed, extremely-balanced gameplay systems that, if you take the time to master them, yield an immensely rewarding experience. The story's almost as complex as the gameplay, but it's well told (one of, if not the, finest examples of writing in a console RPG). The music is gorgeous, and the visuals and direction seep advanced ambition.
Dragon Quest VII: It's long. Very long. But it's one of the best examples on the PSX of excellent classic old-school RPGing. The class system is huge, there are a ton of worlds to explore, and the overall layout of the game's universe and scenario are very fun and both highly original as well as reminiscent of older classic Chrono Trigger.
Tactics Ogre: Still the best SRPG ever made.
Final Fantasy Tactics: Not as good as Tactics Ogre (and in fact it rips off and plagiarizes TO at every availabe opportunity), but it's still very well made and a lot of fun.
Final Fantasy IX: Probably my favorite of the main series PSX Final Fantasies, despite the longer-than-usual loading times / combat intros & outros. It's a Final Fantasy game... you should pretty much know what to expect here.
Grandia: One of the very best turn-based RPG battle systems ever designed (highly strategic, fast, and flexible) combined with a really awesome character development system that ties stat growth to use-to-increase skill in elemental magic and weapon proficiencies. Awesome game.
Suikoden & Suikoden II: More old-school RPGs, but again, two of the finest. Very original in their presentation and progression -- acquire 108 unique characters in each, build and improve/customize your own castle, and play through two of the best stories on the PSX RPG field.
Alundra: Zelda who? This game destroys all of Link's outings in Hyrule.
Arc the Lad II: Probably a somewhat unorthodox choice, but the game is really a blast. Great combat and a megaton amount of quests/sidequests, plus a great number of characters to use. It's also got some nice challenge to it -- some of the bosses and higher level quests can be fairly dangerous.
Star Ocean II: Easily the best of the 2D, and most of the 3D, Wolf Teamesque RPGs (the Star Oceans, the Tales Ofs, etc.). Great combat, branching storyline, different worlds to explore
And on and on and on. Really, the PSX is full of great RPGs; I still think it's the best system for the genre ever.