In no particular order and includes 32X games.
*
Gunstar Heroes - very fun, very intense, visually impressive, chaser+lightning is almost completely OP except that it likes to lock onto non-damaging targets but it still makes the game 8x easier than it should be.
*
Ristar - The swinging mechanics are great, it's pretty, the level design is excellent, it has a water level that you can completely enjoy because Ristar moves better than normal in it, it's excellent.
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Ranger X - Probably the best mech sidescroller I've played. Actually uses the 6 button controller and isn't a fighter. Amazing visuals.
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Streets of Rage 3 - I haven't played enough of 2 to comment on it, but 3 is quite fun, one of my favorite beat-em-ups
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Shadow Squadron - Much much better than Star Wars Arcade, only issue is the energy meter makes clearing later levels very hard. Some of the coolest flat-shaded action around.
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Castlevania Bloodlines - Mostly because it's the one Castlevania I've played the most.
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Musha Aleste [aka M.U.S.H.A.] - Very, very good shoot-em-up. Can be painfully easy or brutally hard, the shield powerup makes things really easy, your hitbox is pretty big though.
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Kawasaki Superbike Challenge - Polygons. Remotely decent framerate. On the Genesis. Fucking yes. Also, a legitimately good racing game.
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Virtua Racing Deluxe - I do like the sense of speed that the SVP version delivers with its low framerate, but VR/32X is the best home version. The PS2 version can fuck off with how odd it handles. VR/32X looks good, plays good, it's good.
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Thunder Force IV - Fucking hard, but so impressive. All that parallax.
I didn't mention Street Fighter or whatnot, because there are better ways to play it [also, I'm an SNK guy through and through

]. There's no reason taking up a slot for a game that can be better enjoyed elsewhere.
Honorable mentions:
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Adventures of Batman and Robin - So damn pretty it hurts. Fantastic soundtrack. Very hard. However, can drag on with how repetitive the enemy formations are, having the same 3 guys thrown at you 7 times in a row isn't interesting. Still, quite enjoyable.
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Alien Soldier - Brilliant game, too fucking hard. Control feels weird.
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Rocket Knight Adventure - It is probably just me. It's a neat game, I just don't rank it so highly.
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Dr. Robotnick's Mean Bean Machine - It's Puyo Puyo. It is not a Sonic game at all. It is amazing and is my favorite not-Tetris puzzle game. The Sonic branding kind of bothers me though.