Mine was Dragon Warrior when I was about 5. It was 'birthday money' but still it was my money. Beaten it so many times I couldn't tell you how many, and I always tried to pit myself against the game in ways it wasn't intended, like trying to get the Erdrick's Sword/Armor at level 7. Lots of dying and retrying... like, lots. But I eventually got Sleep to work against that damned Axe Knight in Haukness for more than a few turns to Hurt him to death, then praying I could exit the town without a random encounter. Fun times.
Soon after that, it was Battletoads. My siblings, both older and younger, always handed me the controller for the 3rd (Blue Racecart) level because no one knew the patterns and underlying mechanics of the game like I did. I was always really good at recognizing and understanding mechanics of games and utilizing them well. Perhaps that's why I do tech support for a living, heh.