Haha, my very first Pokemon Game.. It'd have to be Pokemon Gold. That game was a masterpiece, to be honest though, it wasn't even mine, it was my good friends game, I was only 4, and I borrowed it for about a Month, my Mom was in the hospital for her back, and I played it when I went to visit her.
Later on though, my first ACTUAL Pokemon game ( ACTUAL meaning the one I actually owned myself ) was Pokemon Ruby. All these games didn't seem special at the time because they were just games, but nowadays I look back and Say: "Wow, I actually miss that day I walked through the Grocery Store playing my Gameboy and Pokemon Ruby. "