@Vanellope & Pointblank: That depends a lot on what you're looking for! We've got the stalwart Pokemon Trainer Academy, but perhaps you're not interested in an RP that takes place in a school setting, or an RP that takes place in the Pokemon world. Perhaps you'd like something darker, or something smaller? If you could narrow down your preferences it'd probably be slightly easier for me to recommend something.
For now, all I can do is advertise for my own RPs.
The Pokemon Trainer Academy is a sandbox, character interaction driven pseudo-journey RP taking place on a remote island closest to Kanto with a large fanbase and the strength behind it to help you feel comfortable saying it won't in fact die on you. With a non-competitive leveling system in place, an overarching plot, and the promise that each character will get their own ending to the RP reflecting how they've developed over time you'll have plenty of structure for growing and developing your character amongst your peers while maintaining the freedom to create and lead your own mini plots provided they hold up under basic quality control.
Pokemon Fallout in contrast is a much darker, extreme sandbox RP taking place in Sinnoh where /you/ make the plots and /you/ make your own story. (Or... y'know, follow along as I do the same alongside you.) It's based on a pre-written world in which a human-engineered memetic virus has effectively wiped out Pokemon from the face of the earth. This caused a cataclysm of events that destroyed society and left humanity a shadow of it's former self. However Arceus, being quite out-of-reach of the virus, eventually deemed it necessary to give humanity another chance and reincarnated pokemon in a new form that would be immune to the virus. Pokespirits, as they're called, are quite literally the disembodied souls of pokemon that select children between the ages of 10 and 13 to fuse with, resulting in demi-pokemon humans that wield the full power of the pokemon they've fused with. You play one of these children, to whom the future of the world rests on. It's up to you how you go about using your powers however, and literally nothing is stopping you from dragging the broken world further into it's grave other than your fellow pokespirit wielders.