Sadly, I don't remember my first game totally, I do remember that's a racing game, a cartoon (but not Cartoon Network) racing flash game, I played it a day when I was five (now I am fifteen), my dad said to my older brother: "teach your brother how to play games", because I was didn't know how to use them, he told me the necessary stuff, however it was a little useless; I didn't understand and I try to learn it by myself, at first I wasn't even able to get my character to the track, some days after, I finally managed to win my first race by my count.
The first game that I actually remember is a flash Role-playing game called Epic Battle Fantasy 3, I fell in love with that game, the graphics, the music, the battles I enjoyed it; even it not is too impressive, it's just superior to the common flash games. I played it when I was seven. Now you can play Epic Battle Fantasy 5 free on its developer's page, I really recommend it.