More people should ask themselves this question, I think.

We say, "I have a soul." We also say, "I have a body." What's this 'I', then, that possesses both soul and body?

I think our 'soul' is just another word for our consciousness; but not necessarily a 'sum of neurons'. Actually, it's now theorized that our thoughts and memories aren't stored in our neurons at all -- which would explain why "local lesions in the brain do not selectively impair one or another memory trace" (source:http://www.acsa2000.net/bcngroup/jponkp/); but rather, that the information is stored in the actual impulses that flow between neurons, which act more as conductors. So, what happens to this energy when the brain dies?

Well, we can speculate. The fact that these impulses can be disturbed (people have been legally reported as braindead, and then revived with little or no loss of memory) might be an implication that when we die, the energy doesn't just disappear or disperse. Most descriptions of near-death experiences seem to support this, also.

Maybe if this energy (we could refer to it as a soul, but detatching the connotations of supernatural forces) has an unusually obstinate attachment to the physical body, it attempts to reconstruct it with other energies, which we might percieve as ghosts?