Oh goody! Time to share my favourite SNES games! WALL OF GAMES IN 3...2...1....GOOOOO!!!!
Seiken Densetsu 3. (It's Secret of Mana, but 10 times better. Good story, GREAT combat system, and has a ton of replay value with 6 characters each with their own reasons for seeking the Mana Sword)
Crono Trigger. (It's a freaking LEGEND of a game. AMAZING story, AMAZING combat system, AMAZING EVERYTHING.)
Lufia 2: Rise of the Sinistrals. (It's a DAMN good RPG. It's got zelda style dungeons too. Lots of puzzles. Plus a pretty good story and combat system.)
Super Mario RPG: Legend of the Seven stars. (...just do it. It's hilarious and amazing)
ActRaiser. (a super quirky and weird fusion of genres. You start off in a platforming beat-em up, then go into overhead shooter mode with some building elements, and then to back to beat-em-up mode again for a second dungeon. This repeats for every "country" you restore. It's pretty fun)
UN squadron. (You like space shooters like Gradius? This is pretty much the same thing, but with planes instead. Pretty fun, but HARD AS HELL)
Bahamut Lagoon (Take a strategy RPG like Fire Emblem, and then mix in a turn based RPG system, and THEN mix in a system that allows you to raise your own dragons that will kick ass alongside you in battle. It's GOOD!)
Kirby Super Star. (Need I say more? It's 4 kirby games in one! In fact, forget this one and go get the DS remake. It has even MORE stuff in it!)
Legend of the Mystical Ninja (Pretty fun Beat em up game with silly ninjas)
EVO: the Search for Eden. (You start off as a fish in a large ocean. You kill and eat other creatures. Then you get points to spend on evolving yourself. You then go through many early periods of evolution like the amphibian stage, the dinosaur stage, etc in order to become the strongest creature and reach Eden. Also, abuse your Save States. You will need to. This game is hard and sometimes unfair with how easily you can get hit.)
Terranigma. (I didn't get too far in this game but it's a crazy fast paced action RPG and it's apparently got a kickass story too)
Power rangers the Movie. (DON'T LAUGH! This is a pretty solid Beat-em-up! Trust me, it's fun!)