The cream of the crop like Revenge of Shinobi and Streets of Rage 2 have been mentioned many times over aldeady..........

However...........

The Aladdin game on Megadrive is a completely different game than the one on SNES. (and it also happens to be a very good game too)

https://www.youtube.com/watch?v=ZdrNSu7lxZ0

Aldeady? grrrrrrrrrrr, and i can't even edit posts at work either.......... (already...!!!!)

KLX mentioned Aladdin........... sorry, my mistake. (still, it's completely different so thus the reccomendation)

If you are into schumps:

Thunder Force III and IV

Gaiares

RPGs:

- Phantasy Star II & IV(if you can get a hold of Phantasy Stat I on the SMS it was way ahead of its time!)

 - Phantasy Star II may be VERY grindy and the labyrinths complex for a modern gamer (we used to spend a couple of days leveling up to reach level 56 in order to beat the final labyrinth... that seemed impossible with any lower level back then and unless you mess around a lot you will not be at this level by the time you get there...) still very deep story and world for its time.

 Note on Phantasy Star III - The game aged poorly, the art is not nice and the music less interesting than the rest of the games in the series, however, this game has 6 endings, all tying in to the rest of the Phantasy Star universe, every time spanning over 3 generations, as far as I know no game has done this much in splitting the story (along with denoting the relations between the different factions of people living in this world) all in all it's interesting, just did not age that well.

- Land Stalker

- Shining in the Darkness

- Shining Force I & 2 (more strategy oriented, still considered classics)

Others:

- Streets of Rage 2 & 3 (I don't know why people like the first one, the second is probably the best beat-em up ever made)

- Ranger-X - Great unique mech style game play, amazing special effects, it's a favorite of mine

 - Golder Axe: not as good as the arcade version, but still great early Genesis game

 - Ghouls N' Ghost: pretty hard platformer, great gameplay and music... it does not look as good as the SNES game that came out later, but it's more fun, if only because you can shoot up and down as well as in front and back of your character.

 - Strider: Great platformer, first 8Mb cartridge!!

 - WonderBoy IV: great action adventure game with RPG elements

Any game by Treasure: Dynamite Headdy, Gun Star Heroes

Great decision. I preferred the SNES, but still have a lot of love of the Mega Drive :) There's some fantastic software on it.

Streets of Rage 2 can't be ignored definitely one of the best Mega Drive games ever.

You might find Ristar interesting, that was a fun platformer. Also the likes of Earthworm Jim.

Micro Machines 2 and Turbo Tournament 96 are incredible! Then there were a few great Treasure games like Gunstar Heroes.

Also, although not a patch on the arcade versions but Space Harrier, Afterburner and Outrun are fun.

Streets of Rage 1,2,3
Golden Axe 1,2,3
Sonic 1,2,3
Gunstar Heroes

A couple of awesome titles that are a little more obscure but WELL worth picking up : Target Earth and Herzog Zwei. Zwei is actually a precursor to action RTS stuff.

Mega Man: The Wily Wars. It's a tad expensive though.

Understatement of the year...

Castlevania Bloodlines is a hugely underrated excellent entry in the series. My favorite game released on Genesis.
Vectorman
Columns
All of the Golden Axes
Sonic The Hedgehog 2
Shining Force 2
Comix Zone
Altered Beast