like the majority here, i did not have a Genesis growing up. But, my best friend did, and we played it quite a bit. He also had a 32x and a Sega-CD (and YES, we totally made the Sega CDX!) Here's what i can remember playing at his place (in no particular order, but with thoughts given):
Golden Axe. not sure if he had the 6-pak cartridge or a stand alone Golden Axe, but this is the game we played the most. still love it. i always equate this game with the Genesis because of so many good afternoons, right after getting out of school for the day.
Sonic the Hedgehog, Sonic 2, Sonic & Knuckles. all classics, of course. Sonic 2 was my favorite until the debut of Knuckles, who i immediately supported.
Virtua Fighter. not sure which #, or if this was the 32x version or not. this is definitely not a very good fighting game, although it was hyped as the first 3d fighter. i remember we both got pretty bored by it because we were used to MK2 and SF2, but we amused ourselves by trying to force the other to fall out of the ring. whatever it takes, right?
some boxing game where you could create your own boxer. i wanna say it was Ready 2 Rumble but i may be mistaken there. he had created a fighter named Icicle who was completely blue. we didn't play this one much because he always kicked my ass at it.
Comix Zone. oh man, this game is so friggin' difficult, but a lot of fun. i'm a big comics fan, so the animation and frame-by-frame setup was so cool to see. when i bought a Genesis a year or two back, this was one of the first games i sought out.
and then there was Lethal Enforcers. it sounds awesome, it's based off an arcade game, what could go wrong? the answer: everything. we actively tried to convince ourselves that it was a good game, but it just wasn't happening. it's a shooter game, made for use with those plastic guns. but we didn't have those. so you scrolled around the screen with the d-pad and used a or b to shoot. it was tedious, and stupid, and might have been ok with a Zapper, but just no. So maybe technically not a terrible game, but my experience with it definitely was.