congratulations on buying one of the best systems in the history of video games. With that said here are some solid game choices.
Sonic Series: All the entries in the main game series were very good. you can Skip Spinball and 3D blast as those were not that great. And Dr Robotnik;s mean bean machine is one of the best puzzlers ever.
Streets of Rage 1-3 : one of the best side scrolling beat em ups ever.
Phantasy Star 2-4 : 3 great RPGs that came out on the systems. 3 was quite a bit different than 2 and 4 but a very good entry in the series.
Mortal Kombat : this should be a no brainer. all the gore of the Arcade hit. I know someone said MK2 but honestly I would buy the SNES versions of 2,3 and ultimate over the genesis counterparts.
Comix Zone: A very good Game all the way around.
Vertorman: a decent shooter that has sparked rumors of a 3rd for years.
The Valis Series. these are competent ports of the Turbo versions and a very good action adventure series.
Golden Axe 1-3: still fun after all these years.
After Burner - A jet shooter that will have you feeling like you are in Top Gun
Hang on - Classic Racing game
Thunder Blade - See After Burner but with a hellicopter
Rastan Saga 2 - great action game.