What kind of games do you like? The SNES really has good games for a lot of genres.

In addition to super mario world (my favorite mario game) you also should grab
Super Mario All Stars
And Super Mario RPG
The Legend of Zelda: A Link to the Past is amazing and in my opinion the best SNES game period (although I do admit that nostalgia may effect this but I replay the game atleast once a year)
Donkey Kong Country 1&3 are awesome but my favorite is 2
Super Mario Kart is freaking sweet and was amazing when it came out, but if you've played Mario Kart 64 (still my favorite) you'll enjoy Super Mario Kart but probably not be impressed by it.
Star Fox is also a very fun game on the SNES but I liked Star Fox 64 a little bit more (but I'm a weird Star Fox fan as my favorite so far is Star Fox Assault)
It's hard for me to recommend any of the other games I have for the SNES because of the fact that they are not widely known/loved. For instance I imported (the only time I've ever imported anything) every DBZ game I could find for the SNES and learned to play them despite not knowing the language, but this is because I love DBZ (Hyper Dimension is an amazing fighter, and The Legend of the Super Saiyan is a great RPG). You might like mortal kombat but those were big during the SNES/Genisis era and without that nostalgia I'm not sure they would hold up.

If you actually read all that I also want to say congrats on getting an SNES it is an amazing system and please (for the love of god!) in real life either call it the Super Nintendo Entertainment System, the Super Nintendo, or the S. N. E. S. (as in pronounce each letter) I've only heard 1 person in real life call it the snesss (as in the character Ness with a nasalized s at the beginning) and it is horrible and apparently in other parts of the world it is common - but I hate it.

I know its already been mentioned before, but please go and get Chrono Trigger.
also, Super Metroid, FF6(3), Link to the Past,Super Punch-out,Contra 3, Super Gradius,The Megaman games...actually, cant think of many SNES games you shouldnt get

^Shaq-Fu, is one SNES game you probably shouldn't get.

Most of the great SNES games are either cheaper or just plain better on another format.

I say go for the games that can only be found on the SNES like TMNT IV or Earthbound.

so many good games already mentioned, i'll just have to put down uni-racer (uni-rally) and equinox

uni-racers will have your eyes melting and your ability to see colours destroyed in five minutes

The SNES had the best lineup of games ever. There's thousands of good ones. All of the ones mentioned are gold! Get your hands on Pilot Wings if possible and Breath of Fire I and II are good RPGs too.

I rented this game like a billion times when I was a kid.. I hope it comes out for VC one of these days..

The Legend of Zelda - A Link To Past -

Unless you're a huge fan of E-bay, and saving games that can't save anymore (due to dead batteries), you're probably better off just getting a Wii and using the Virtual Console. But since that song came out saying "Ain't Nothing Like the Real Thing, Baby", people have been believing that, so........if you can find them (and good luck with that), there are some pretty good lists in this thread already. All you really need is Tetris Attack, though.