Hah, what a thread for me! The 16-bit era still holds a place in my heart.
Genesis: (don't have much games for it, even now, but here's what I like)
Sonic the Hedgehog: I'm pretty sure that it was the first game I ever played, back in 2000 or something. Everybody had their fancy new three-dimensional video games at one-twenty-somethin' bits while I enjoyed my nice 16-bit Jenny (my Genesis' nick) on a usual day...
Aladdin: Of all my hatred towards movie-based games, this is probably the only one I like. Yah, sad.
I only had 8 games for the Genesis, but they're great ones.
SNES: (I didn't have my very own SNES, but my grandma had one, now it's my aunt's, and I loved the crap out of it)
Super Mario World: What do I have to say for this? Instant classic. It took the awesomeness of SMB3 and duplicated it at least 50 times.
Donkey Kong Country: One of the games that has it's own cozy place in my heart, and the one I simply love the most. Diddy Kong's Quest was alright, but 3 just wasn't the same, and repeated the kidnapping crap for NO REASON. >_> The GBA port was also the first game I ever owned myself, with the GBA SP being the first game system I ever owned myself.
I can't quite remember anything else that really stuck out in my grandma's SNES library but those obvious two.