First game I remember...pfew. Well when I was a little kid, like 4-5 or something, we had this pre-DOS computer. On it was some wierd game wich was simply a big shooting target and a moving dot. You had to hit the spacebar to 'shoot' (wich simply ment the moving dot stood still) and then your score was calculated, including the number of 'shots' you fired. Every time you had a succesfull hit, the dot moved slighly faster, and faster, etc etc untill it became really difficult. I remember playing it sometimes while sitting on my dad's lap, when we still got along hehe
After that we got a DOS computer with stuff like Commander Keen, Duke Nukem (the 1st!).