The first video games I can remember playing were my dad's copies of the original Super Mario Bros. and Ghosts n' Goblins. I enjoyed Super Mario Bros. only mildly at the time and, at the age of 4, found Ghosts n' Goblins too tough (and scaaaary). However, I later came to love both of them; especially Ghosts n' Goblins.
The first game that really got me into this medium was the original Metroid, which I played for the first time the following year. The heavy emphasis on exploration in particular proved a strong drawing card for me. I played for almost four hours solid the first time until my dad finally made me give him the controller back.