This is a tough one to answer, since I have memories of gaming from as far back as I can remember. The first one I remember playing was something on the Atari that resembled Adventure, but I don't think it *was* Adventure unless my memory of it is pretty distorted, as I remember being a white knight fighting black knights rather than a square fighting dragons.
The next thing I remember was my bro and his friend playing Wizards & Warriors on the NES, and being stuck on the big bat boss. They decided to put me on the game as kind of a joke, and despite not having a clue what I was doing, I beat the big bat pretty effortlessly, much to their surprise. "Keep playing!" they insisted, but after that I kept falling in lava and couldn't get out.
Once I started to really understand how to play games, I played a lot of Super Mario Bros, Legend of Zelda and Super Mario Bros 2, but I think the first series I would say I really became a "fan" of was Mega Man. We used to rent those a lot, parts 2 through 6... never did experience the first one until the emulation age. Not sure if I beat any of them back then either, I know I did get to the final boss gauntlet in one of them once and then my thumb gave out and I had to stop.