When I was starting to play games as a kid Western RPGs, Action RPGs, First Person Shooters, and Strategy games weren't really too popular (not even existed in the case for FPS and RTS games). I used to play a lot of 2D Platformers, Beat-em-Ups, JRPGs, and Zelda back then. I still like Zelda I suppose but I barely started playing Twilight Princess and I don't have a Wii so it doesn't really matter.
Most defining game for me was probably Diablo or more-so Diablo II when I got really into it, Baldur's Gate 2 to some extent as well. I was already in High School though when I played those.