Ok since we have knocked out quite a few selections, I'm going to compile a list.
I'll list quite a few of the well known games and what other people have mentioned. Probably forgot a bunch but it's late and I'll adjust.
SOME OF THE BESTEST SNES GAMES
Chrono Trigger
Super Mario RPG
Shadowrun
Final Fantasy II
Final Fantasy III
Final Fantasy V (Emulator/Translation)
Illusion of Gaia
Terranigma (Emulator/Translation)
Soul Blazer
Paladin's Quest
Secret of Mana
Seiken Densetsu 3 (Emulator/Translation)
Secret of Evermore
Earthbound
Dragon Quest VI (Emulator/Translation)
Dragon Quest V (Emulator/Translation)
Treasures of the Rudras (Emulator/Translation)
Breath of Fire I
Breath of Fire II
Lufia I
Lufia II
Uncharted Waters
Flashback
Out of this World
Twisted Tales of Spike McFang
Donkey Kong Country series
Castlevania IV
Dracula X (Castlevania)
Zombies Ate my Neighbors
Knights of the Round
King of the Dragons
Aladdin
Legend of the Mystical Ninja
Blackthorne!
Harvest Moon
Romance of the Three Kingdoms IV
Ogre Battle
Pocky and Rocky
Joe & Mac
Gradius III
Axelay
Ogre Battle
Starfox
Super Punchout
Lost Vikings 1 & 2
Sim City
Legend of Zelda: Link to the Past
Demon Crest
King Arthur and the Knights of Justice
Live a Live (Emulator/Translation)
Wing Commander
F-Zero
Super Mario World
Pilotwings
Villgust
Star Ocean (Emulator/Translation)
Tales of Phantasia (Emulator/Translation)
Romancing Saga 3 (Emulator/Translation)
Front Mission (Emulator/Translation)
Bahamut Lagoon (Emulator/Translation)
Treasure Hunter G (Emulator/Translation)
E.V.O Search for Eden
Jurassic Park games
Kirby's Avalanche
Rock n Roll Racing
TMNT TURTLES IN TIME
Tinstar
Metal Warriors
Megaman X games
Doom Troopers
Super Bomberman
Super Metroid
Rocky Rodent
Super Buster Brothers
Mega Man Soccer
WWF Super Wrestlemania
Super Ghouls n' Ghosts
Super R-Type
Battletoads in Battlemaniacs
Battletoads and Double Dragon
Kirby Superstar
Actraiser games
Super Mario Allstars
Earthworm Jim
Clay Fighters
Killer Instinct
TMNT Tournament Fighters
Street Fighter II
Street Fighter II Turbo
Super Street Fighter II
SFA II
Super Empire Strikes Back
Super Return of the Jedi
Tecmo Super Bowl games
Demon's Crest
Tactics Ogre (Emulator/Don't think the translation is complete since they do have a English PS version)
Super Double Dragon
Metal Warriors
Hagane