I remember having beaten the elite four for the first time.I nearly belted out the pokemon theme song,as my beloved Charizard came on screen (The only survivor after the Champion battle) and the credits roled. :D
Another great moment was when I finally got past that weird (slightly creepy) guy (old dude) who kept trying to get me to buy his candy bars. (It took me months to figure it out,by then I had beat blue version,)
Plus,who could forget that amazing moment when you get your first pokemon.