Lot's of goodies already listed.
I'll second (or third, fourth, whatever):
Castle of Illusion
Gain Ground
Golden Axe
Gunstar Heroes
Lightening Force (yes, the game is mis-spelled)
Streets of Rage 1 & 2
Thunderforce III
Vectorman
Wings of Wor
Wonder Boy in Monster World
I didn't see these listed already but I wasn't really paying attention.

Beyond Oasis
Final Zone (I like it, may not be everyone's cup o' tea)
Forgotten Worlds
Hellfire
Revenge of Shinobi
Sol-Deace (hard as nails but has lot's of neat graphical things going on)
Sunset Riders
Steel Empire (Fun steam-punky shootie)
Virtua Racing (I don't know if this would run on one of those everdrives, but it's pretty impressive to see all that 3d on the Genesis)
Twin Cobra isn't nearly as good as Kyukyoku Tiger on the PCE, but it has a pretty boss soundtrack.
Dragon's Revenge is Tengen's miserable attempt to make a sequel of Devil's Crush/Crash. It's pretty bad, but probably worth checking out if you're into Devil's Crush (and who isn't?)
I've also put way too much time into Flicky. :oops: