It's always easy to forget just HOW GOD DAMN MANY RPGs they were for the Playstation. Yes, Japan always had a lot of RPGs, but once the PS1 hit in the States, and FFVII sold a lot, that's when we began to see a veritable flood of RPGs over here. I could make an entire post out of just PS1 RPGs, really.
Anyway...
Arc The Lad series: The PS2 sequels not so much. But anyone who, like me, bought the gigantic Working Designs boxset of the original three PS1 games knows how great this series is. I played through all of 1 and 3, but 2 just dragged on too long for me. Someday I plan on going back and playing through all three games again. Imagine if Sony had actually released this before FFVII in the U.S. rather than relying on pieces of shit like Beyond The Beyond to fill the PS1's RPG library for the first year or so of its existence...
Front Missions series: I've only ever played through Front Mission 3, but what I messed around with the other games was quite fun despite the language barrier. It's a turn based strategy RPG only with mechs. You get to customize them, so think Armored Core meets FFT.
Xenogears: No, not Xenosaga. I know a lot of people hate this game, think its second disc is awful, pretentious, and boring...but man do I love this game. Yeah, it's clearly influenced by Neon Genesis Evangelion--despite the denials by the developers--and the plot is incomprehensible for the most part, but still a surprising deep and interesting game.
Tales series: These games are really hit or miss, but Tales of Symphonia was one of the best reasons to own a Gamecube. I love real time battle systems that have a feel of balance and polish, and this game has that in spades.
Suikoden series: These games are unfortunately hard to find, at least the beloved Suikoden II, anyway. Many fans seem to hate Suikoden 3 and 4, but I myself devoured 3 back in the day. It was the best RPG after FFX on the PS2 for awhile.
Star Ocean series: Again, another great RPG franchise that delivers at least passable RPGs every time. Star Ocean 2 was a pretty big deal back in the day; I know a few people who still bust this out and replay it every so often.
Shining Force series: My best friend and I have a borderline obsession with Shining Force 1 and 2, to the point that we rented Shining Force 2 so many times that we may as well have just bought it back in the day. A few years back he actually bought a Saturn and copy of Shining Force 3 off eBay, which was really good but just not as fun (or, obviously, complete) as the first two games. The games that they keep releasing with the Shining name are a mediocre tragedy compared to how amazing this series used to be.
Mana series: What a troubled path this series has walked!! Secret of Mana is still the best known in the States, though its Japan-only sequel (Seiken Densetstu 3) is legendary amongst those who have played it. I fondly remember Legend of Mana for PS1, though I also remember it being childishly easy. The modern day games in this series are forgettable and bland, sadly, and everyone longs for a next-gen, online capable remake or full fledged spiritual sequel to Secret of Mana.
Ogre Battle series: I know the last game in this series to be released was for N64, but still. Tactics Ogre for PS1 was all but wholesale ripped off by Square to make FFT, which says a lot about how underrated and influential this series was.
Grandia series: Like Star Ocean and Tales, Grandia has a rep for being "that other RPG series" that certain segments of the population obsess over. Grandia II was one of the best reasons to own a Dreamcast, but they eventually ported this game to other systems (I wanna say it was for PS2 and Gamecube, but that doesn't sound right). Like those two series, it has a real time battle system and its own unique feel and gameplay/skill systems.
Phantasy Star series: Anymore all we get is Phantasy Star Online-type games, but back in the Genesis/Master System era, this series was like Sega's quasi-rival to Final Fantasy. I always felt that these games were technically impressive in their day but are now unplayably bland and tedious. My friend who shelled out for Shining Force 3 also bought a used copy of Phantasy Star 2 for Genesis and we both regretted that decision.