Usually, I play around with the after-game. When that's done, I'll other restart (of course, trade over everything to another game), or keep it and playthrough again on another Pokemon game (be it of an older generation or the counterpart of the current one).
After a while, I'll be happy with a team and play around with it, trying to level everything up. That fades over time and I'll try new Pokemon. Sometimes I'll get the urge to complete the Pokedex, but it comes and goes.
Lately, I've been trying to get more into the more advanced mechanics of Pokemon. Competitive Team Building, IV Breeding, EV Training, etc. I've been building a Trick Room team for the VGCs, and I've been breeding Pokemon for other people as gifts. I play on the Battle Subway periodically, and I plan to start going on the Random Match-Up soon.
When that gets a little too much, I'll play an older game, or I'll play like, Pokemon Rumble Blast or something. A mini-game, or the Wii offshoots (Battle Revolution, Colosseum, Pikachu's Pokepark, etc.). If not, I'll settle for just talking about Pokemon.