Super Mario rpg and seiken densetsu 2 and 3. Incredible games, the lot of them. Pay
You might wanna play crono cross if you haven't. I know it's PlayStation, but it's definitely worth your while.

beat me too it

Honestly, after Chrono Trigger, I recommend taking a break to savor how amazing it was.

Be sure to do the sidequests!

Terranigma!!

Get it, play it and love it!

You're probably still missing out on a lot of overlooked PSX games.  Like Brigandine for example.  

I made a list a long time ago of localized RPGs in the west for both SNES and PSX to compare how many titles were released on each system.  There are unlocalized games for both PSX and SNES(both having fan translations like Dragon Quest 3,) but listing games released in the west only is easier.  It's broken down between non Squaresoft games and Squaresoft games.  Missing some games from both lists, both games that are RPGs that I may have missed and games that I don't consider RPGs(Castlevania Symphony of the Night, Illusion of Gaia, Legacy of Kain Blood Omen, Alundra, Dragon Valor, etc.)

Arc the Lad
Arc the Lad 2
Arc Arena
Arc the Lad 3
Azure Dreams
Beyond the Beyond
Breath of Fire 3
Breath of Fire 4
Brigandine
Darkstone
Diablo
Digimon World
Digimon World 2
Digimon World 3
Dragon Seeds
Dragon Warrior 7
Eternal Eyes
Grandia
Guardian's Crusade
Hoshigami
Kartia
King's Field
King's Field 2
Koudelka
Legend of Dragoon
Legend of Legaia
Lunar
Lunar 2
Monster Rancher  (worth playing but you summon monsters with discs so might want to play the GBA games.)
Monster Rancher 2
Monster Seed
Ogre Battle
Persona 2 Eternal Punishment
Revelations Persona
Rhapsody(or Chrapsody
Saiyuki Journey West
Shadow Madness
Shadow Tower
Star Ocean the Second Story
Suikoden
Suikoden 2
Tactics Ogre
Tales of Destiny
Tales of Eternia
Thousands Arms
Torneko the Last Hope
Valkyrie Profile
Vandal Hearts
Vandal Hearts 2
Vanguard Bandits
Wild ARMs
Wild ARMs 2

52 games.

Chocobo's Dungeon 2
Ehrgeiz(Forsaken Dungeon)
Final Fantasy
Final Fantasy 2
Final Fantasy 4
Final Fantasy 5
Final Fantasy 6
Final Fantasy 7
Final Fantasy 8
Final Fantasy 9
Final Fantasy Tactics
Chrono Trigger
Chrono Cross
Front Mission 3
Parasite Eve
Parasite Eve 2
SaGa Frontier
SaGa Frontier 2
Vagrant Story
Xenogears

20 games.

SNES titles. Again titles that I wouldn't consider as RPGs won't be listed.

7th Saga
Brain Lord
Brandish
Breath of Fire(Squaresoft published, Capcom developed.)
Breath of Fire 2
Dragon View
Drakkhen
Dungeon Master
Earthbound
Eye of the Beholder
Inindo
Lufia
Lufia 2
Might and Magic 2
Magic and Magic 3 (SNES version is slow, play PC version)
Ogre Battle
Paladin's Quest
Robotrek
Shadowrun
Super Mario RPG(Squaresoft developed, but a Mario game.)
Super Ninja Boy
Tecmo Secret of the Stars
Terranigma
Ultima the False Prophet
Wizardry 5
Ys3

26 games.

Chrono Trigger
Final Fantasy 4
Final Fantasy 6
Final Fantasy Mystic Quest
Secret of Evermore
Secret of Mana

6 games.

I won't ruin anything and hopefully no one else does either, but I'll say you'll see for yourself. 

I'm afraid I'm not much of an authority -- I'm far behind on RPGs on all platforms -- but I highly recommend finishing Final Fantasy VI on SNES. It's arguably the best turn-based RPG ever made.

The SNES era was the Golden Era of rpgs as far as I'm concerned.

Breath of Fire, FF IV-VI, Mystic Quest, Chrono Trigger, Dragon Quest V-VI, Mario RPG, Secret of Evermore, Illusion of Gaia, Soulblazer, Terranigma, Secret of Mana, etc.

Hell, even Genesis had great rpgs around that same time, like Light Crusader, Shining in the Darkness, Shining Force 1-2, Beyond Oasis, and Phantasy Star II-IV.

Check out Bowser's Inside Story or Partners in Time for the DS. Not the most in depth RPGs and they can be somewhat simplistic but they're pretty fun overall and have some good humour.

I would have to say Dragon Quest (IX), Final Fantasy (IV), The World Ends With You or simply Pokemon for the DS.

Though, yeah if you have a Wii, get Xenoblade. What an excellent game.