Not including PC games.
For me, it was Sonic the Hedgehog 3 and Sega Genesis. I received them for Christmas 1996, when I was 8. Basically, I think my parents bought the console on clearance, since Saturn was out at that time.
Anyway, that's why Sonic will always be special to me, since it was my first gaming experience.
I'd love to hear from others about their first gaming experiences too.