Like the NES, the SNES also has a number of romhacks to improve and/or modify a game's aspects or make an entirely new game on the game's engine, sometimes with new graphics and music. Some of these "new games" tend to be quite the challenge, so approach with caution. Everything else should explain what you're getting into just fine.
Super Mario World
VIP Mario (series)
Those silly VIPpers on 2ch decided Super Mario World wasn't hard or looney enough. So they made a series of romhacks until they were satisfied. Examples of stuff to expect: StageBoss
A modification to FF2us that adds a new script and changes names to be more consistant with FF6. If you want a more authentic experience, you could use Namingway Edition which adds full spell names like Blizzard and original Hard Type maps.
This fucking rocks. This is for those who wanted to beat entire stages and bosses as Zero instead of just briefly using him like in the original. The best part is swapping to and from X and Zero non-stop after the intro stage (or even at the stage select), reminiscent of Xtreme 2. The sole exception being boss fights which lock you into your current character until death or victory. Instead of just being an overpowered X, Zero is like an alternate version, as there's some stuff X can do that he can't, along with the buster shots being different. Also, X and Zero share armor parts, sub-tanks, and weapons, but not lifebars or heart tanks, so keep that in mind. There's also some other tweaks to things here and there which you might enjoy or may even not notice.
Hyper Metroid is yet another retelling of Super Metroid, and one that does a fantastic job. The best hack with the lamest title, based on Project Base and some other stuff (ever wanted to combine spazer and plasma legit? you can! it'd shred enemies if they didn't have a fuckton of health by the time you can!) Best played when you want a breath of fresh air and a map layout, as well as item order. Very open feel to it, and great level design. 8chan is/was mildly obsessed with this hack.
Super Metroid Redesign 2.1 FINAL (Axeil Edition 1.4)
Action / Adventure
Super Metroid: Redesign is a total overhaul of Super Metroid. "The Planet Zebes, now bigger than we've previously seen it, is filled with many mysteries. Sleeping within the depths of the planet is a secret heavily protected by the last standing symbols of the great Chozo race..." PROTIP: If you like this, you'll definitely enjoy the library to be found at Metroid Construction. D-D-DOUBLE OFFER: An update by Drewseph is in the works under the name of Super Metroid Redesign: Axeil which updates the level design based on a certain speedrunner's game design criticisms. UPDATE: AXEIL EDITION IS OUT! Get SMRA here!
Project Base is kinda hard to pigeonhole. It's an update to the graphics (new tiles and palettes) and physics (enhanced regular physics and some cool new additions) of Super, and has some minor adjustments and additions to the level design. Now comes with several on/off flavor switching for people who like to customize and tweak. A speedrunner's wet dream and a great way to re-experience an SNES classic. Has its own speedrunning leaderboard!
Romancing SaGa 3, but completely remade with new bosses, music, quests, and characters from all other SaGa games (So far there are a total of 80 or so quests and that's counting the original quests in Romancing SaGa 3 and new things are still being added to this day). It even features the Combination System from SaGa frontier onward. Only in Japanese though, however there are videos online of segments you can follow if stuck.
Secret Of Evermore is a good game, however it has issues; one being weapons do not have a shared level. This Patch fixes most of the problems present in the original game, making it more enjoyable gameplay wise.
You like Zombies Ate My Neighbors (but possibly not Ghoul Patrol) and you want more? This is exactly that, and quite good too! Almost 10 years in the making, a complete hack/unofficial sequel including 55 all new levels, new gameplay options, items, enemies and more!