Pac-Man 2: The New Adventure, and probably Sonic 1. These are the earliest memories I remember. I actually barely remember playing either, and I also barely remember the period that I had a Genesis, but I have very specific and narrow memories of these games, The first stage of Sonic of course, and a point in Pac-Man where you get slammed in a door that's opening.
The majority of my early memories are with the Playstation, games like Frogger, Blasto, and Crash Bandicoot.