I didn't have a Genesis back when it was still going. But I remember playing games like Sonic, X-Men, and TMNT Hyperstone Heist. Most of my Genesis experience came from buying a used Genesis in the PS1/N64/Saturn era, and then from emulation. There's a good number of sweet games to play.
TMNT Hyperstone Heist may not have been TMNT Turtles in Time, but it was a fantastic Genesis game. Warsong is another great game because its actually Langrisser localized into english. Der Langrisser for the SNES was translated by fans as well as Langrisser II for the Genesis which never made it over here. It's a neat strategy RPG. Predator 2 was another game I remember from back when the Genesis was still going. A friend of mine had it. Those 3 red dots were always creepy.