>>2740853EarthBound is definitely a top candidate. The third post in this thread (bazoo.png) mentions a bunch of games I never played, save for Ogre Battle. I assume he means March of The Black Queen, as I don't remember playing anything else, and when I was about 8-10 I tried it so it didn't sit as well with me as it would today. I remember liking it, but not trying much to understand it. That said, it's probably up there as a great game, though I think it's mainly strategy, not RPG, so I wouldn't consider it anyway. Still a game worth playing.
I grew up with Squaresoft games, so I would always stand by Chrono Trigger, Final Fantasy VI (III in the states at that time), Final Fantasy IV (II in the states), and a few others by Square as greats. Maybe not "best" but they still are enjoyable, even without nostalgia goggles. The mechanics and gameplay at the time were fun, and still fare well. Story is the generic stuff but you can't expect too much from ANY RPG (JRPG or otherwise), aside from a few titles.
As an aside, those few titles that stand out to me with great storytelling are Xenogears, Persona 3, Phantasy Star IV (the entire premise and plot is wonderful, even if they didn't have a lot of memory or budget to work with - the actual idea is quality sci-fi, even if it has been done a lot by now - at the time it was a very novel idea), Suikoden II (again, expanded it would make for a great plot and story, similar to Game of Thrones [books and early show] were it to ever be allowed to breach some of the more PC limits of modern day), and some others that I know are there, but which aren't coming to mind at the time.
If you don't care for story, but just want good gameplay (and to see some titles I haven't seen mentioned for SNES), try Robotrek (Enix, before it merged with Square, and a very fun game overall (story was shit, but mechanics were great), Secret of Evermore (Secret of Mana but with a dog companion as your only other member) and...