My sister pointed me to this video about a particularly interesting split-brain experiment. In these experiments, the corpus collosum, the bundle of nerves that connects the two hemispheres of the brain, is surgically severed, usually as a treatment for severe epilepsy. The result is literally two separate brains residing in the same body, which can develop two separate personalities. In this case, one of the personalities believes in God and the other one doesn't. As the speaker observes, this raises a profound theological question: what happens when this person dies? (And no, saying this person has two souls doesn't solve the problem, because that just raises the question of when he acquired his second soul.)
Personally, I believe this is just an extreme case of what is actually a much more common phenomenon than is generally appreciated. Our conscious selves are not, in fact, the coherent whole we perceive them to be. The perception we have that we are "individuals" with an "essence" or an identity that is constant across time or even coherent at any given moment is an illusion. This can be demonstrated by a wide range of psychophysics experiments, but I don't have time to look those up at the moment. Fodder for a future post. Someone remind me.