Pokemon Gold was the game that got me hooked on gaming as a source of entertainment when I was a kid, and even if it's kind of boring to me now, it still holds a special place in my heart for it. Besides that, Oddworld: Stranger's Wrath was the first game to make me realize that games could actually have interesting characters, plots, and settings the same way movies and books did (I'm super-excited for the HD re-release on PSN, by the way). So those two are what I'd consider to be "my games" in the definition you've outlined.