It was either...Asteroids, or the Mortal Kombat, back on the Sega Genesis. Can't remember, that was a long time ago, and Dad had gotten it for himself (which is weird, since he doesn't seem like much of a fighting game enthusiast, more of an action-adventure type).
The first game I remember playing any significant amount was Ocarina of Time. I recall thinking "this is a pretty long game!"...after finishing the Deku Tree. That there were two more sections astounded me. And then the Temples showed up...
It ended up defining alot of my gaming loves, that's for sure.