It's all about Smogon
No lame story, no gym badge bullshit, no breeding or leveling up. Pick your dream team, punch in the EV values and set them to level 100. Give it any 4 moves it can legally learn, and then battle with people online.
One of my old dream teams had a charizard that was more or less unstoppable: substitute, belly drum, fire punch and ice punch. It had some berry which, combined with belly drum, would bring the bastard down to 25% HP and give him stupid bonuses to both speed and damage. Ideally, all of this behind a substitute.
Pokemon's combat may not have flashy animations (and I think they should re-boot the series from a three dimensional third-person viewpoint), but the nitty gritty details about guessing whether or not your opponent will switch pokemon and give you a free attack actually *mean* something when you're using awesome teams.