I was watching the Doublefine Adventure project videos, and remembered how much I played Gilbert's Freddi Fish and Putt-Putt games when I was a kid.
Also Commander Keen, Captain Comic, The Incredible Machine (For some reason I'd always try to torture the cat in every way imaginable) and later Giants: Citizen Kabuto.
I also remember playing http://www.youtube.com/watch?v=uZDG4dlU5uY. Looks like I played that about 13-15 years after it came out (I'm from 1991). I had no idea, I wasn't concerned about graphics.

Later there was HoMM 2 and 3, I played a lot of 3 with my brother.
And of course, Golden Sun on the GBA! I remember waiting for the sequel when I finished the first.
It's funny how early on my parents introduced me to all sorts of games, my parents aren't gamers themselves at all.
Edit: And the first Prince of Persia on DOS! I remember killing the final boss with my eyes closed on later playthroughs. I can go on with this forever.