I came up with a character whose power is that he has two bodies. He was born with two bodies, so naturally, his parents assumed he was two people, twins, but that isn't the case. He perceives the world through both sets of senses simultaneously. Though he has a single mind, he does have two brains, which means he can multitask easily, learning two things at the same time. In combat he employs a unique fighting style using both bodies in concert, in effect fight back-to-back with himself, but in perfect coordination.
The connection is based on quantum entanglement, and isn't limited by distance. It's theoretically impossible to cut them off from each other without rendering one of the bodies unconscious.
However, when one of his bodies is knocked unconscious, his other body becomes relatively useless as well. He's too used to having both brains, and the controls for any one body are distributed between both brains, so the conscious body has some almost stroke-victim-like affectations in this state.