Check out this article on MSNBC. By stimulating a certain part of the brain, scientists can induce someone to believe there's a shadow person just behind them. It's really just a projection of their own body slightly dislocated by their minds. But it leads to interesting new questions and things to explore about schizophrenics (not multiple personality disorder, which is what many people seem to think schizophrenia is), and stories of alien abduction or control and even simple (or not so simple) paranoia.
I think it could also be an interesting premise for a story. Many ways to take that--that there really are these shadow people following all of us around, but most of us don't recognize it could be one fun direction to take. It could be a guardian angel, or something more malevolent. Yeah, I just wanted to use the word 'malevolent.'