Not counting my very first game (Boulder Dash), which was technically my first favorite because there wasn't any competition

Anyway the first ones that lasted a while was a toss-up between Legend of Zelda and Mega Man 2. I spent a lot of time on those two games on my NES. I can't really tell which one of the two was my favorite, because this was at the tender age of 4 and my memory from that time is extremely vague.

Since then there's pretty much a new favorite every couple of years.