Here is my top 10. Five through ten are subject to change depending on my mood and how recently I played a game.

I decided to limit it to one game per series, but obviously if one game is good, there's a good change other games in the series are good.
10. Streets of Rage 2 (beat-em-up)
9. Monster World IV (side-scrolling action RPG)
8. Phantasy Star IV (turn-based RPG)
7. Rocket Knight Adventures (platformer)
6. Castlevania Bloodlines (chain-whipping platformer)
5. Castle of Illusion (Disney platforming goodness)
4. Alien Soldier (run-n-gun platformer)
3. Shinobi III (ninja platformer)
2. Thunder Force III (horizontal shooter)
1. Sonic 3 + Knuckles (one-of-the-best-games-of-all-time platformer)
Runner up: Road Rash 2
Many of you are probably questioning why I put SoR2 last. Well, the only reason Streets of Rage 2 is on here at all is because how amazing it was at the time, and how awesome it would have been today if it were not for Streets of Rage Remake. I find it hard to revisit the classic series with SoRR out. But if you've not played any SoR game, then by all means, play 2. In fact, play SoR1 first!
Just a couple of games can't make it to the list because I've never played them. These include Crusader of Centy and Ranger-X.
Some I played just enough to know I like, but not enough to go top 10 just yet, like Beyond Oasis. I'll revisit it when I have time. :-"
Others I didn't give a fair shot on the Genesis because they were better elsewhere, like Zombies Ate My Neighbors, which looks and sounds much better on the SNES (despite muffle); also included here are Mortal Kombat II, Street Fighter II, and Phantom 2040.
I'll defend my list, although I'm a bit bummed more shooters didn't make it into the top 10. Some like Gaiares, MUSHA, and Gleylancer vie up there.