Pokemon for the Gameboy Advance. Perfect Dark for the N64. Wild Arms for the PS One. I played the Atari 2600 and the NES, but didn't really like any games on them. For me, the magic started with Playstation, Gameboy Advance and N64.
Edit: When I amd my Brother were kids, we got a playsation for Christmas/Birthday. (My Birthday is December 2.) I had played games for along time, since I was a very, very little kid, but I moved to Arkansas without actually owning a game system. We eventually got an Atari 2600 and a NES from relatives as hand me downs. We kept bugging Grandma/Mom for a Sega Genesis/Saturn, we didn't even know that Playstation existed. We got Playstation from our other Grandmother, who we never saw...and it was amazing. It kept freezing until we turned the damn thing upside down, but when it finally worked, it was magical. I still get a flood of feelings when I turn on my PS3, play a PS One game, and see the PS one symbol and music.