The very first game I ever played was my father's copy of Crash Bandicoot 2 for the Playstation. The first game I ever owned myself (not including some silly Mickey Mouse game) was Super Mario Bros. Deluxe for the GameBoy Color. ^_^
I had never heard of or played a Super Mario game before. The only reason I bought it was because I had recently played another GameBoy game at a friend's house and got addicted to it. I didn't know the name of that game, all I could remember was that the main character was dressed in green, so I was looking for boxes that had characters clad in green. I finally saw a box with one on it (Luigi) and I thought it was the same game. I soon learned it wasn't, but it was extremely fun so I decided to keep it. So in essence, I stumbled upon one of the most popular games of all time by accident XD.
Years later, after I had become a Zelda fanatic, I realized that game I played at my old friend's house was Link's Awakening =P