First game ever, and I will never forget: Super Mario World for the, "Super Nintendo". I have fond memories of me watching my dad play it, and a little 3-year-old me walking off cliffs because I didn't know how to jump.
Super Mario Bros (NES) was the first game I ever came into contact with by watching my brother play it, and we played the co-op game (and like every woeful younger sibling, I had to be Luigi). As for my first very own game that was only played by me...my memory is a bit fuzzy, but I think it was the first Spyro for the first Play Station.