I am somewhat biased towards the more new-school cinematic JRPG, (which I think has really fallen out of fashion this generation) but that doesn't mean that I don't have a soft spot for SNES games. These are my favorites:
PS2: The PS2 didn't win me over completely until I played the Digital Devil Saga games. Now it's my favorite system of all time. As with the PS1, there are tons of notable games that I haven't played for it yet.
1) Digital Devil Saga 1 & 2: I've always liked Xenogears and Xenosaga, but this series seems to be a similar style of RPG, only with the best turn based battle system I've ever seen in a non SRPG. I haven't found an RPG with a story that I've liked more since. As far as the psychological/religious aspects to the game, they are far more integrated into the game world, and consequentially don't come of as pretentious at all. (at least to me)
2) Persona 4: Another exceptionally great game by Atlus. I liked the blend of dating sim, rpg and visual novel elements in the game. The fact that the game lets you control your entire party is a big plus over Persona 3...
3) Final Fantasy XII: My personal favorite combat system in any Final Fantasy game.
4) Xenosaga Series: Say what you want about it, but I really liked this series. There were some genuinely great characters in these games, such as KOS-MOS, and Shion's brother.
PS1: I got into the PS1 late, since I stubbornly stuck with the N64 exclusively until PS1 emulation became well known. I haven't had the chance to play any Atlus games for the system, so my list could change substantially. I regret not getting into the system far earlier, since it has hundreds of great RPGs in it's library.
1) Xenogears: This game truly set the bar for stories in a RPG, for all of its flaws. I always look for games similar to this (at least in my perception) every generation. It never felt finished, and the gameplay was just average, but I felt like it set new standards for what games should be allowed to say or do.
2) Final Fantasy VII: Obviously a historically significant Final Fantasy game, it's hard to downplay its signficance on gaming.
3) Final Fantasy VIII: A lot of people didn't like this game, but I loved the combat system and the atmosphere of the game. The characters were quite an acquired taste, but the art direction of the environments was excellent.
SNES: The game system of my childhood. (also the NES, but that system didn't quite have as great of an RPG library) I really thought that the SNES took what the NES did well, and improved on it in every way possible.
1) Final Fantasy VI: Probably my favorite Final Fantasy. Personally my favorite cast, and a massive one too. Set the formula for Final Fantasy VII. (It seems to me that Final Fantasy VII, for all of its greatness, is very similar to VI) Had a cinematic feel in the game engine, even though it had no FMV cutscenes.
2) Secret of Mana: My favorite RPG combat system of all time. I'm suprised it hasn't influenced more games to date.
3) Final Fantasy IV: My first mainline final fantasy game. (Yes, I started with Mystic Quest, and I actually liked the game) There are many boss fights in this game that make me feel like it was just yesterday. There is something about this game that I can't describe, just a visceral appeal to it.