The constant in all the media, at least, is psychic power. So far we can count the big-power psychics on one hand, and most other psychic powers shown are limited to mild telekinesis (lifting Pokeballs), psychic empathy, or by-admission spotty precognition. We may presume other and similar weak abilities may exist, just because they don't impact the setting much and wouldn't wildly throw the balance of things.
The other known abilities are similar in scope. Exorcism relates to ghost Pokemon, is based on a pop culture wide-eyed view of the world, and doesn't dramatically affect the setting. There's been some presence of magic in an episode or two of the show, as I recall. It's capable of weird stuff (Pokemon-human transmutation), but nothing that Poke-science can't do (witness: Bill).
The important detail concerning these supernatural abilities--psionics, exorcism, and even some magery--is that it doesn't disrupt the main focus of the setting, which is capturing collectable whatsits via superior technology. Superhumans aren't more prominent because it'd overwhelm the setting, like mecha and steampunk tend to do. Witness the various superpowered Mary Sues for an example of this in action.
Now, here comes an idea. Supernatural skills don't seem to impact the setting much. But... what if psi powers and magery are in fact vital to the setting? Not the flashy stuff, of course. Silph Co. develops teleportation square technology based on psionic teleportation. Potions are old magical cures converted to spray bottle format. The chime of a Pokemon center's healbox is a purifying ritual played on midi, no tribal dancing required. The like.
Again I am denied a good transition to the ending. With that admitted--what are your collective stances on the supernatural in Pokemon? Should there be more? Less/none? How could superpowers be integrated into Pokemon without overwhelming the Pokemaspect? Speculate wildly.
EDIT: Additional topics I've not yet touched on: Supernatural creatures that aren't Pokemon and the interaction therein, public opinion of superhuman abilities, origins of supernatural abilities, and new special abilities that wouldn't be out of place in a Pokegame.
