For some reason I randomly have the urge to play some quality SNES and GBA RPG's, so please post your personal favorites or critically acclaimed ones for each system please.

You spelled "Quality" incorrectly. Qulaity...

Super Nintendo
Chrono Trigger
Super Mario RPG

GBA
All DBZ Legacy of Gokus
Something Reveria
Fire Emblem

SNES
Terranigma
Earthbound
Treasure Hunter G
Dark Law: The Meaning of Death
Illusion of Gaia
Bahamut Lagoon
Dual Orb II
FEDA: The Emblem of Justice
Jutei Senki
Treasure of the Rudras (Rudora no Hihou)
Secret of Mana
Seiken Densetsu 3
Chrono Trigger
Final Fantasy IV-VI
Soul Blazer
Secret of Evermore
Star Ocean
Tales of Phantasia
Romancing Saga 3
The Legend of Zelda: A Link to the Past

GBA:
Final Fantasy I & II: Dawn of Souls
Golden Sun
Golden Sun: The Lost Age
The Legend of Zelda: The Minish Cap (not really an RPG though, just like all the other Zeldas)
Riviera: The Primised Land
Yggdra Union: We'll Never Fight Alone
Summon Night: Swordcraft Story 1/2
Kingdom Hearts: Chain of Memories
Mario & Luigi: Superstar Saga
Fire Emblem: The Sacred Stones
Sword of Mana

Agozer pretty much hit everything I would think of.

The only one I could say for Snes is probably Front mission.

Nm I got some for GBA:
Shining Force
FF tactics
One of the megaman battle networks: Play one you played them all

I feel a serious lack of drive to start thinking of titles, but you MUST play Tecmo's Secret of The Stars on SNES.

This is one of my fav RPGs ever.

Think I downloaded Secret of the Stars way back when I first got into emulation, I remember liking it.

EDIT: Almost forgot, thanks for the list guys.

Final Fantasy games
Phantasy Star Collection

Anything Pre-FF7 is good.

Yeah, because it's the true FF feeling, that the newer releases are missing!
But I'm really looking forward to the Wii and DS ones... will buy them when they are released I think!

Back to the list, there are nearly all already said, but I will also explain why:
SNES
------
*Soul Blazer & Soul Blazer 2: Illusion of Gaia - both really great games, with good story, nice quest and a long and exciting gameplay
*Secret of Mana - 3 Player Multiplayer Fun on the SNES! DO I have to say more? I've bought these f*cking adapter only for this great game!
*Mario RPG - The All time classic! Collaboration between Sqare and Nintendo! A true and great RPG with the alltime franchise Mario
*Lufia 2: - Never played one, but this games has a great story, superb gfx and and very brain crushing puzzles! ANd I can level up as long and as often I want and the enemies are still very strong! O.o
*Chrono Trigger - Better than any FF IMHO! Nearly 10 different endings, Adventure Plus, a lot Techs, Spells, characters, great story, wonderful chara design (Akira Toriyama) and a lot more! Give it a try!

Probably I will also add some GBA games, but atm, I don't feel like... O.o

How could I have missed Lufias on both the SNES and GBA? There is also a Lunar game on the GBA, although not nearly as good as the Sega CD originals or the PSX remakes.

Yeah, Super Mario RPG is one of those games you have to play.

So yeah:

For GBA:

Lufia: Ruins of Lore
Shining Force: Resurection of the Dark Dragon
Lunar Legend

and

Lufia & The Fortress of Doom + Lufia II: The rise of the Sinistrals on the SNES.
Breath of Fire 1/2

SNES:
Breath of Fire
Breath of Fire 2

Forgot how awesome FF tactics advance was for the GBA. Anyone else enjoy this game?

Yes, as I generally enjoy T-RPGs.

Other good GBA tactics-RPG games:

Onimusha Tactics
Tactics Ogre: The Knight of Lodis
Shining Force - Resurrection of the Dark Dragon
Zone of the Enders: The Fist of Mars

i'd mention might & magic 2 or 3 on super nintendo, just as western rpg examples. they're kind of slow and clunky in combat, but obviously the advantage with an emulator is you can turbo through enemy phase.

main reason i refer them, despite lack of visual character design and awful sound, is as far as rpg's go they're the closest i've played to combining the party structure of eastern rpg's with the free form development (story and acessable game world) of western rpgs (elder scrolls etc).
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i hope in the future i get to see better realised hybrid rpgs, with party development akin to ff5 or ffTactics and the freedom of exploration seen in western games.

Kingdom Hearts. ^^

The Megaten games, now called persona I believe. There should be translations for the snes ones.

Shin Megami Tensei and persona are different series. Persona is a spinoff of sorts from Megaten, though.

Yeah you're right. Well I heard those games are good.

Shin Megami 1 is, unfortunately, horribly glitchy in AGTP's english translation (it wasn't what you'd call thoroughly beta-tested). SMT2, however, has never given me problems.

Now, onto listing...
SNES:
Dragon Quest 1+2, 5, and 6
Chrono Trigger
All FF's
Rudora no Hihou (Treasure of the Rudra's. AGTP did an awesome translation on it)
Star Ocean (biggest SNES cartridge ever. Dejap did a good job on it, though the yes/no choice graphics are still in Japanese. Also, you'll need to use their utility to decompress the graphics. or ZSNES won't run it right)

GBA:
FFTA
Demikids (Megaten may have predated pokemon by nearly a decade, but this is obviously a pokemon clone. However, it's storyline kicks far more ass. Help Lucifer save the world from the evil ruler of heaven (you don't even want to know how THAT happened))
Sword of Mana
Golden Sun 1&2

And an nes one, why not?
Musashi no Bouken (Adventure of Musashi. it has great dialogue like "I will defeat Kojiro, and maybe even get laid!")

Not really. ZSNES has had the S-DD1 decompression chip emulation implemented for a good while now. IIRC, from 1.42 onwards. No graphics packs nor external utilities are needed.

Really? I'd heard it was so, but never got around to testing it because my copy was already decompressed. I figured it, like the cake, was a lie.

In any case, I forgot to add one of the greatest SNES RPGs of all time to the list: EarthBound. Yes, EarthBound. Do not underestimate the Starman.

thanks for reminding me of that games existance

I agree. Damn those douches at Brownie Brown/Nintendo for not doing an official translation for Mother 3.