One game I'm pretty sure hasn't been mentioned: Unirally (also known as uniracer).
I spent my childhood playing ultima, civiliasation, super mariokart, sim-ctiy and unirally. Unirally is probably THE most underrated game on the snes.
Unirally is a 2d side-scrolling unicycle racer. Fast paced and requiring reasonable dexterity it can be an extremely frustrating game if you don't stop making that exact same mistake over and over and over again. You play as a personified unicycle, that is either up against a single computer controlled opponent or in split screen multiplayer .As is common in most racing games, you have groups of tracks (mario-kart 'cups'), with more 'cups' opening up if you win some. The game has a seriously arcade feel, with the colors and sounds bound to drive the adrenalin. There are no use-able item power ups, but some features of the track can be positive or negative (slowing slime, speed boost arrows).
However, if you perform a trick and land it (like pushing jump and holding the shoulder button to perform a forward roll and chucking a twist in for pro-ness) then you get a small speed boost. Also, unlike most racers, 1 out of the 5 tracks per 'cup' (i think they use leagues) is a stunt track, meaning that you need to perform enough tricks to achieve a certain score to pass the stage. Of course the point value of these tricks have diminishing returns, although different combinations of the same tricks will still score well.
There is also a progressive difficulty change. if you beat the introductory level unicycle (bronsen - bronze medal) then you gain access to the medium difficulty level (sylvia - silver medal). The game really takes an interesting twist once you have access to the higher difficulty opponent and the harder tracks.
Once you are at the hardest difficulty level (i think his name is goldwyn - gold medal) you are racing against a dirty - no holds barred opponent. This uniciycle is some sort of magic evil genius-cycle as he has powers to really make life difficult for you.
Invisible track, backwards controls, background moving in a non logical direction to confuse you are just some of the tricks he can inflict on you with no warning - just a cackling laughter and message on the screen at the precise moment that the effect occurs. this in itself can be disorientating as your mind flashes between "oh no, that laugh, he's done something" to "whoa writing, wait, what did it say" and "where the hell did the track go". These effects seem to be used sparingly on the easier tracks (only the hardest difficulty cycle opponent has the abilities), but once you get to the last sets of tracks then he pulls out all the stops.
The learning curve is not very steep, although to master the game requires a great level of skill. Even though there are lots of races to be had to finish the game, each win still feels satisfying.
This game is right up the charts and probably the best snes game not containing mario or zelda.
