I'm not a huge jRPG fag, but I have a few personal favorites, partly based upon nostalgia, but also based on titles that are slightly underrated or posses unique qualities. I can't recommend any new titles since I haven't played many in recent years.
Earthbound - quirky, funny, cute and most definitely one of the top RPG's for the SNES. If you haven't played it, I recommend it. There aren't many games like it.
Vagrant Story - more of a dungeon crawler really, but the story is really compelling with a very unique crafting and combat system. It has ties (loosely) to the Final Fantasy Tactics series - which is also worth playing - so it adds a little flavor to the lore. Probably one of my favorites by Square for the PS1.
Final Fantasy V - I bet you thought I would say 6?! I always liked 5 since I played it on the PS1. The job system was new to me at the time, the world was fairly open for exploration, and it had several location that were totally optional. I was hooked. X-Death was one of my favorite villains at the time.
Legend of Mana - There is a deep crafting system that isn't explained very well in this game. The art is unmatched on the PS1 only by Saga Frontier 2 - as far as originality goes - almost like a water color painting, that is still impressive to this day. It has real time combat that features 2 players. I never played Secret of Mana so I wasn't disappointed by the game like some were.
Super Mario RPG - One of those unique titles that will never happen again. Nothing mind shattering as far as story goes, but it is funny at times, with some adult themed jokes related to Princess Peach. Good stuff.
Persona 4 - didn't play much of it, but I know it is good. I plan on the playing the newer one (for the vita I think it was?) for sure.
Shining Force 2 - one of those classics that is worth playing to check off the old list. I plan on beating all of the classic "must play" jRPG's at some point before I die. It's my duty to catalog the decline and incline across the various sub-genres...for historical purposes of course.
Dragon Quest 7 - I've wanted to play it for so long, but it has been out of my reach. I have never played any of the games in this series, but I have experienced the combat via Earthbound.
I don't think Chrono Trigger is all people make it out to be, but I missed it at the time it came out, so the nostalgia holds no sway over me. I just wish the story was a little better. Final Fantasy 6 is good but I think a bit overrated. 8 gets shit on but it is more compelling than 6. Some of the romance stuff was a bit gey but it was the first game I ever maxed levels on so it holds a special place in my heart. Final Fantasy 7 is a love/hate thing with me. I never was a fan of the story especially when they started messing with it after the fact. I never bothered with the Tales series since it looks too "anime" for me. The newer Final Fantasy games are trash to me. Final Fantasy 10 started the decline. Once graphics entered the modern age, away from sprites and into the anime heavy crap I dislike.