Despite being a huge Sega fan, most of my experience comes from the Master System; I didn't own a Genesis until much later, and most of the games I played were rentals. The top games on this list were actually the ones that pushed me to buy the console above all else.
10. Garfield: Caught in the Act
9. Aladdin
8. Sonic the Hedgehog 2
7. Contra: Hard Corps
6. Ultimate Mortal Kombat 3
5. Jurassic park
4. Sonic 3 & Knuckles
3. The Lost World: Jurassic Park
2. Ecco the Dolphin
1. Ecco: the Tides of Time