I found this thing called SNESbox.com, and it's basically an online Super Nintendo emulator, that lets you play games in your browser. However, I had a problem with the game window not fitting completely in the.... box thingy.
TO PUT IT IN A SIMPLE WAY, my Mario was running around without me being able to see anything below his chin and I probably couldn't see stuff on the right side as well.

Maybe it's just me, my browser or something like that. Maybe it's just that game. However, I guess it's worth a try. To be honest, I never had a Super Nintendo, only the Nintendo 64.

Link; http://www.stumbleupon.com/su/1zObIw/snesbox.com/

So let me know, did it work for you? Did you have fun?