I was too young to finish any of my NES games, which consisted of Mario 1-3 and a bunch of Capcom titles, but damn playing all those games really cut my gaming teeth.
The first game I ended up beating was Sonic 2, which was much easier than those NES games. Though it was still a good challenge to beat the final zone, two bosses in a row with no rings. I died many times learning the patterns, and had to play the whole game over from scratch to get there again for weeks. I was 7.
Edit: I didn't spot the Genesis tips book at the Scholastic book fair until a few years later, so I had no idea about the level select or Super Sonic codes yet, which blew my mind after all the time I spent getting back to the final boss lol.