Okay, I'll exclude games I still own on the original system (FFVI, Chrono Trigger, Earthbound), games I own as a port (Mario 3, A Link to the Past, Mario 64), games that I once owned and sold because I didn't care anymore (Kirby's Dreamland 3, Tetris & Dr. Mario), and games that I once owned and sold only because I knew I'd be able to download them back on Revolution anyway (Kirby Super Star, Super Mario RPG).
In no order:
1)
EVO: The Search For Eden (SNES). The game was brilliant, though the concept was really,
really out there. (A great summary of why can be found
at GameFAQs, of all places, albeit spoiling the story to do so.)
2)
Zombies Ate My Neighbors (SNES). Of all the games that I only played because of the recommendation of a casual-gamer relatives, this is the only one that turned out good--and boy, did it ever turn out good.
3)
Super Metroid (SNES). This and Metroid Fusion are the two games in the series that I've never owned. I've played Super Metroid, though, so I know how worthwhile it is.
4)
Terranigma (SNES). I liked Illusion of Gaia.
5)
Mario Tennis (N64). I didn't find out how brilliant this franchise is until the GBA game.
6)
Ogre Battle (SNES). Apparently I'm in the minority considering how this thread has gone, but I vastly preferred this to the N64 sequel; both the battles and the walking speed were faster in the original SNES game.
7)
Actraiser (SNES). A friend rented this long ago and I thought it was a great game.
8)
Beetle Adventure Racing (N64). I've heard good things about it, and comparisons to Diddy Kong Racing. Considering that I think single-player DKR blows all single-player Mario Kart games out of the water, that's a nice comparison to make.
9)
YS, any of them (TG16). I saw screenshots and the screenshots involved cute anime females and an RPG, thus making this a must-buy.
10) I have no idea what the name is (TG16). Basically a vertical-scrolling space shooter that looked fantastic, but the website where I saw a picture of it is currently down, so I don't know the title...