Chrono Trigger
Megaman X
Final Fantasy 6
Demon's Crest
Harvest Moon
Super Mario World 2: Yoshi's Island
Zelda: A link to the Past
Super Metroid (never really played it, but everyone circle jerks over it so it must be decent)
Tales of Phantasia
Killer Instinct (if you're into fighters)
There are other games that used to be good but no point in playing on the SNES. For example, Street Fighter 2 was awesome but you can play it on so many platforms that there's no point in opting for the SNES version. There's also Mortal Kombat but who really played those because they were "good"? If you have another person to play with, Kirby Super Star and Battletoads & Double Dragon would be worth checking out.