Gunstar Heroes is my favourite game on the system. I'd consider it one of the best games of all time. You should look for it.
Battletoads is a great game.
Sreets of Rage 1, 2 and 3 are all good, 2 is the best.
Columns is cheap and very fun.
Mercs is a fun shooter.
Probotector is good.
Castlevania The New Generation is another good Konami game.
Xenon 2 is a cool shmup
Space Harrier 2
Ghouls N Ghosts
After Burner II
These and for some lesser known titles:
Nadia: Secret of The Blue Water
Rocket Knight adventures + Sparkster
Shining in the darkness + Shining force
Crusader of Centry
Treasure produced the best games on the system, such as Alien Soldier and Gunstar Heroes. Even their lesser discussed titles are excellent. Make sure to try Mcdonalds Treasure Land Adventure, it's terrific and it's a damn shame that most people gloss over it as either an inferior version of Dynamite Headdy or a simple promotional game.
Oh and if you're into fighters, you have to try Yu Yu Hakusho: Makyou Toitsusen. 4-player fitghter with great moveset and charaters.
Mega Turican is great but hard to find
Ecco and Pocahontas are beautiful and relaxing
Toejam & Earl.
Make sure to play the first Sonic.
Jurrasic Park and Flashback still has decent atmosphere
tmnt: hyperstone heist
road rash 1-3
streets of rage 2 & 3
mortal kombat 1 & 2
phantasy star 4
toejam & earl 2: panic on funktotron