If you are new to the Sega Genesis and you got your emulator up and running, or if you want to try new games. Here is a list that the users and I recommend for ya.

Action:
Alex the kid
Bio-hazard Battle
Castle of Illusion Feat Mickey Mouse
Castlevania Bloodlines
Cool Spot
Comix Zone
Double Dragon III
Ecco The Dolphin 2: Tides of Time
Gadget Twins
Ghouls n Ghosts
Golden Axe
Golden Axe 2
Hell Fire
Marbel Madness
Mickey Mania
Mega Bomberman
Mortal Kombat 2
Mortal Kombat 3
Quack shot
Ranger X
Shinobi 3
Sonic the Hedgehog
Sonic the Hedgehog 2
Sonic the Hedgehog 3
Sonic & Knuckles
Streets of Rage
Streets of Rage 2
Streets of Rage 3
Super Smash TV
Target Earth
Toe Jam and Earl
Vectorman
Vectorman 2
X-men
X-men 2
Zero Wing
Zombies ate my neighbors

Adventure:
Beavis and Butthead

Driving:
Road Rash 3
Lotus 2

Fighting:
Eternal Champions
Fatal Fury 2
Samurai Showdown
Super street fighter 2

RPG:
Phantasy Star 3
Phantasy Star 4
Shining Force
Shining Force 2
Vermillion Sword

Sports:
Mutant League Hockey
NBA Jam
NBA Jam Tournament Edition

If you agree or disagree with this list or want to add entries. Post because as you can see, Some sections need help
Super High Impact

How about Sparkster/Rocket Knight. That was pretty cool.

Splatterhouse games: 1 & 2 have very poor playability, but the third is very playable. All are quite twisted and scary tho!

Micheal Jackson's Moonwalker is another good one.

Shadow of the Beast games are always great, whatever the platform. Again, they are very hard.

And Skitchin is one great rollerblading game! It roxxors!

General Chaos
Gunstar Heroes
Primal Rage (graphics suck, but it's better than the SNES port)
Star Wars 32X (not sure on the actual title, plays kinda like starfox, 2 player coop in a Y-wing)
Virtua Fighter 32X

I like playing all the sonic games, Altered_Beast, Samurai showdown, Beavis and butthead, DragonBall Z, Battle Toads, Clay fighter, for laughs i like to play Micheal jackson Moonwalker, Shining force 1 and 2, Rockman MegaWorld, soleil.

Mega Turrican is a good one for action fans. Also worth noting are:
Chaos Engine
Dragon's Fury
Earthworm Jim 1 and 2
Jungle Strike
Urban Strike

Im a big fan of RoadRash, and me thinks Road Rash 2 is the best of the series. Steering and music are better than in part 3, and the bikes dont look like glued in afterwards.
Besides that you people forgot the Urban/Desert/Jungle Strike series, and ofcourse Landstalker, a highly underrated Action-RPG, Zelda-Style but Isometric view.

I don't anything can beat Sonic the Hedgehog 1 what I heard from is it was the best game ever.

I've recently found Twinkle Tale (J) to be quite an enjoyable game. It's a shooter game sort of like Ikari Warriors for NES, but with medieval/fantasy RPG-like graphics/characters. It features power-ups and special "weapons".

Correction. I didn't have this game so I looked for it. It is actually known as

Sword of Vermilion

My list of Sega games is real small, so I'm hoping this gets the job done. Thanks for the recommendation!

hahahaha I had an obsession with ToeJam & Earl. Ranger X was pretty awesome.

Golden Axe, Streets of Rage, X-Men, and Shining Force are among my top tier Mega Drive games.

Many of these games are available on the Genesis Collection, for both PSP and PS2 (neither of which should cost you more than $15). I have the PSP version, personally, and the emulation is seamless. I'm quite amazed as to how good these games still look even with an LCD screen to show off all of the pixelation.

Shinobi III = Ninja on surfboard. Need more be said?

EDIT: Game list for Genesis Collection --

1. Alex Kidd in the Enchanted Castle Released in 1989
2. Altered Beast (Genesis/Mega Drive and Arcade versions), Released in 1989
3. Bonanza Bros. Released in 1990
4. Columns Released in 1990
5. Comix Zone Released in 1995
6. Decap Attack Released in 1991
7. Ecco the Dolphin Released in 1993
8. Ecco: The Tides of Time Released in 1994
9. Ecco Jr. Released in 1995
10. Flicky Released in 1991
11. Gain Ground Released in 1991
12. Golden Axe Released in 1989
13. Golden Axe II Released in 1991
14. Golden Axe III Released in 1993
15. Kid Chameleon Released in 1992
16. Phantasy Star II Released in 1989
17. Phantasy Star III: Generations of Doom Released in 1991
18. Phantasy Star IV: The End of the Millennium Released in 1994
19. Ristar Released in 1995
20. Shadow Dancer: The Secret of Shinobi (unavailable in the PAL version) Released in 1990
21. Shinobi III: Return of the Ninja Master Released in 1993
22. Sonic The Hedgehog Released in 1991
23. Sonic The Hedgehog 2 Released in 1992
24. Super Thunder Blade Released in 1988
25. Sword of Vermilion Released in 1990
26. Vectorman Released in 1995
27. Vectorman 2 Released in 1996
28. Virtua Fighter 2 (Genesis/MegaDrive version) Released in 1996

You forgot Phantasy Star 2 in the RPG part, it's much better than part 3.

If you can find it try megaman: the wily wars, only released on sega channel, but i did find it for japanese megadrive on ebay for a mere 120 dollars. lmao

HF-

The Mickey Mouse games for the Genesis were kinda cool.

gunstar heroes(play the gba sequel gunstar super heroes as well).
contra hard corps
comix zone
ghoulsnghosts.