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.