I never really bought games with my own money until I'd left home. Before that, I'd always just gotten games as gifts on my birthday or for Christmas, or sometimes as a reward for doing quite well at something that was a big deal (winning a piano festival, good grades, etc.).
As a result, the first game I bought with my own money wasn't until 2009 when I bought Assassin's Creed II. I bought it a week after release and it was worth every penny. While the next three games of the series were nothing special, ACII is was one of my favourite games of all time.
Also, I should mention that I never buy a game at full price unless I'm sure that I"ll enjoy it a lot. This means that I've usually tried it at a friend's house first, or simply seen lots of reviews and gameplay of it.