A lot of moments come to mind, but right now I'm thinking of two:

When I was four years old, my older brother gave me his Yellow cartridge. I'd played around a bit on his games before, but it was the first game that was actually mine, y'know? Anyway, I'm playing and cannot for the life of me figure out how to catch a Pokémon! I wanted a Mankey so badly, but every time I beat a Pokémon I'd go all the way back to Viridian City to check my PC, and there'd be no Pokémon in there! Finally I got frustrated and decided to go through Viridian Forest with just my Pikachu. Eventually my older brother noticed my difficulty and he showed me how to catch Pokémon by helping me catch a level four Nidoran(M) in the patch of grass south of Pewter City.

Another was when I got Crystal and I COULD PICK A GIRL TO PLAY AS. Whenever I played Pokémon in the past I always imagined that my character was a tomboy or disguised as a boy like Mulan, but Crystal let me play as an actual girl, no excuses!