Team Rocket (May have been listed already)

I think that Team Rocket should pop up somewhere around your map every now and again. And, they should be attempting to catch a wild pokemon that is classed "Rare" so you fight them. If you lose, then Team Rocket receive the pokemon (Team Rocket should also be around the same level as you, if not, probably less.) If you succeed, Team Rocket get blasted off again and the pokemon either wants to be caught by you or allying you like in some games or movies where a legendary comes from the sky to help the supposed trainer in distress. Thanks for reading my suggestion

~Dr. Monty