I think my first game I ever got was a Felix the Cat sidescroller... some of the soundtrack still sticks in my mind to this day.
The first game I bought for myself, by myself was probably Call of Duty Black Ops... I really wanted the game and I had to ask someone who was over 16 to go in and buy it for me, and I hid it from my parents because they wouldnt let me play those games til a few years later.