People with amputated limbs sometimes experience the presence of a phantom limb which continues to exist where their old limb was-- they can perceive pain or temperature changes in the missing limb, and have a sense of its orientation. It seems like this is probably caused by lingering activity in the parts of the brain which previously processed such sensory data coming from the limb.
Well, it turns out that it's also possible to experience a supernumerary phantom limb: for instance, one Swiss woman reported feeling the presence of a pale, translucent third arm following a stroke. Researchers have found that this woman's brain treats the arm just as it would a real one-- when she uses it to perform a task like scratching an itch, an MRI of her brain shows activity in regions corresponding to her sense of touch, as well as activity in the visual cortex from where she perceives the arm's presence. And it relieves the itch where she'd scratched it, too.