Well, technically it would be one of the Amstrad games that I played with my sisters, we had a Winter Sports Game, a Summer Sports Game, Ghostbusters, some kind of PI game, Hangman, etc. My first console game, however, was Super Mario Bros. 1
It's shrouded pretty heavily in the mists of time, but I remember at some point in the fall of 1985 we had made the trek to see my cousins in Wisconsin, who had an Atari. I'm fairly certain Missile Command was the first game I played, and I failed miserably.
I'm not sure if it was the first but I have a very early memory of me playing Hugo's House of Horrors. That's right folks, I used to play games that required a parser for you to be able to do anything. Because of that, I also clearly remember failing miserably every time I tried to play it to completion.
Another prominent memory I have from about the same time is Sim City. I can't say for sure which game I played first but these two stick out in my memory so it must have been one of the two.
Close second is Ocarina of Time. Does helping someone else who's playing, but not holding the controller yourself, count as playing? If so, OoT would be the first game I completed. My dad did the playing part.
I think it was Kirby's Dreamland 1 or 2, I loved those games (and still do). My mom got my sister a Game Boy Color and me a Game Boy Pocket because I was very young and she wasn't sure I was old enough to figure it out, but I got the hang of it very quickly. Also, my Game Boy Pocket came with Dr. Mario but I switched it with my sister for Kirby because Dr. Mario was too hard at the time, haha.