It was a SNES game, I'm pretty sure of that, but which one I don't know. (I was about 4 at the time)
I think it was either Super Mario World or The Legend of Zelda: A Link to the Past, I remember playing those.
I also remember playing Yoshi's safari with a super scope.
We might of had Dungeon Master, and Pilotwings as well. And Super Probotector (aka Contra 3) as well. And Donkey Kong Country.
(I must of been very young when we had it, because I was born in 1991 (And we traded the console in to get a N64 sometimes around its release))
I know the game that got me hooked on gaming and that was Pokemon Blue.
Playing that game to the extreme, even as a child, kind of sparked a flame that hasn't been extinguished yet!
EDIT: I had a Mega Drive as well. I remember having Lion King and Sonic, (we sold it at some point, then we got another one from my uncle).