Uh...I think it was the first Mario game on the original Nintendo. I don't remember playing it as my first game, though. The first game I remember, which was my favorite for a long time, was Bubble Bobble.
The story of how Mario was my first game is kind of cute, actually. My mom and dad had just bought it and the original Nintendo and would play Mario taking turns during the weekends and ordering pizza. I was super little at this time, probably 3 or 4. I would always watch them, but any time they offered me the paddle, I'd run away screaming down the hall. This happened for probably 3 months. 3 months of me just watching them every weekend. Well, one day, they woke up and found me already up, playing the game. And quite well, too, from what I hear.