Wobbuffet's tail. According to the Pokédex, it is desperate to keep it hidden. Many people have theorized why, and the popularly accepted theory is that the tail is the Pokémon and the part we believe is the body is really just a puppet.
But here's an alternate theory:
There are two Wobbuffet (at this point, Wynaut) in a single egg. Within the egg, they are entirely black, without a speck of blue on them. However, the unique chemicals in the egg's yolk causes the Wynaut's skin to turn blue, slowly but surely.
However, the Wynaut within the egg fight an ongoing battle. The stronger Wynaut will be the one to ingest most of the proteins and chemicals within the yolk, with only enough for the sibling to be able to barely survive. However, they do not live very long unless they attach themselves to the stronger sibling, slowly sucking just enough proteins from them to stay alive.
As a Wynaut, the sibling that feeds the other is uncaring for what it often considers to be a parasite, pressing itself against other Wynaut in hopes to suffocate the sibling, or become strong enough to crush the pest itself somehow. In some cases, this works. However, the Wynaut is usually killed afterward by predators, as when it is alive, the sibling sees everything coming from behind to hurt the Wynaut and warns it through the use of what little psychic ability it has. Without this extra protection, the Wynaut is quickly killed when it stumbles into the land of a predatory Pokémon.
However, in most cases, the tail will survive until the evolution of the Wynaut into Wobbuffet. In this stage, it is often more intelligent, and its abilities to speak psychically with its sibling improve greatly. The Wobbuffet will gladly spend much of its day in dark places talking with its sibling, making sure its sensitive tail goes unharmed by the light. When it must go into the sun, the tail is shaded by the blob-like bag of skin hanging off the back of its 'head.' It will spend most of its days protecting the family member, letting it slowly leech off of them until the day the Wobbuffet dies.