top games:
Shadow Dancer (fucking love this game)
Shinobi 3
Ranger-X (I wish the cave level wasn't so early in the game, otherwise, this is such a cool ass game; you'll want a 6 button controller for the best experience)
Sonic 2, Sonic 3&K (Sonic 1 isn't that bad either)
Gunstar Heroes
Castlevania Bloodlines
MUSHA (almost put this in the below list, it's good, but has some weird design flaws)
Phantasy Star 4
Streets of Rage 2 (1 is okay, and western releases of 3 got fucked up)

other games I like
Kawasaki Superbike Challenge (cool graphics, feels good to play)
Out Run (there are better ports now, but I have a soft spot for the Genesis version)
Granada (slightly janky top-down tank game, but I love this one)
Space Harrier II (very jank launch title, but I think it is fun)
Road Rash (I think it's jank now, but it is a classic for a reason)
Rocket Knight Adventures (some would put it in the top list, but it never quite hit those highs for me)
Super Hang-On (runs slow versus the arcade version but is still fun, has a neat home mode with upgrades too)

others (things not released in the US)
Alien Soldier (kicks ass, if you can't beat the first boss, the game is actually doing a hard check on if you know how to play and you should up how the teleport dash and reflect mechanics work)
Super Fantasy Zone (why the fuck didn't this come out in the US)
Battle Mania: Daiginjou (we got the first game as Trouble Shooters)

I'm missing a few, but here's something to work with.