I remember buying a few games on impulse when I was 8 and again when I was 10 or 11. Beyond that, I've always done my research before I buy games.
The first time was when I was given 10 dollars for some reason, and decided to spend it at the used everything store. I had no clue what games were good or not, but I wanted to buy something just so it could be mine, so I bought Kirby's Dream Course and Gradius III. In the end I liked both, and in particular I have fond memories of playing Kirby's Dream Course with my siblings. (It's a Kirby themed Golfing game where Kirby is the ball. Strangely it's the only Kirby game I've ever played.)
The other time that I remember is when, for some reason I had a copy of Pokemon Ruby, (Got it as a gift or as a contest prize, I can't remember.) and since I didn't own a GBA and my parents definitely weren't going to get me one, I had to trade it in at the local Wal-Mart. I traded it for a Finding Nemo game, and Harry Potter and the Chamber of Secrets, which I loved. I thought the former would be a platformer, but it turned out to be more of an interactive storybook. I grew up with living books type games, but I had outgrown them by then and was disappointed.