Gunstar Heroes - if someone asked me what my favorite game of all time was from the day I played this in the early 90s until now, this would be the answer. I don't think I need to say any more.
Alien Soldier - obviously did not play this when it was new because it didn't come out in NA, but it's an incredible game all the same. A tough learning curve, but I can't think of a 2D sidescroller that gives you control of a more powerful player character. It's everything great about Genesis action games.
Contra: Hard Corps - total insanity to me that Contra 3 gets far more recognition than this. It's the best Contra game. Hard as balls, but fair as you have plenty of tools like the slide and general bullshit from Browny if you use him. The branching paths make it great to replay, I don't really consider myself a speedrunner but there was a time when I liked this game enough to speedrun/1 life it on certain paths. Music is extremely badass too.
Thunder Force 4 - I didn't play this until this year, when I found it at a yard sale (as Lightening Force). I couldn't put it down, it's a tough challenge but not impossible and is just really well designed. It has that 'magic' to it. Oh and one of the best game soundtracks I've ever heard helps a bit.
Rocket Knight Adventures - found this one in a Blockbuster bargain bin when I was a kid. There were ads in comic books that made it look cool and it was $5 so why not. Best $5 I ever spent.
Phantasy Star IV - Honestly if you like RPGs and haven't played this you kind of suck.
Sonic 2 - mostly a nostalgia thing I guess. Probably played this more than any Genesis game.
Shining Force 2 - been a real long time since I played it, but I loved it back then. I might give it another run through.
Shinobi 3 - Not much to say, just a kick ass game.
S3&K - pretty much obligatory.
Notable other games:
Streets of Rage 2 - I'll be honest I haven't played it all that much. But I've listened to its soundtrack more than I've played a lot of games.
I still haven't played Castlevania Bloodlines, I'm saving it for next week. Castlevania in October is kind of a thing I do.
I LOVED Road Rash 2 as a kid. Haven't gone back to it since then, doubt it holds up much though.