If on the other hand the soul is seen as something which is necessarily immaterial, then I do not believe in it. Hypothetically, should someone make an exact replica of me, with the exact same atoms in the exact same places, nothing more would be required. The replica and I would be impossible to distinguish from each other. The replica would react to any stimuli like me, would have the same childhood memories, be attracted to the same things, and just like me the replica would be disgusted by the smell of an orange.
This would not last long though. If me and my replica would continue our lives, then gradually subtle environmental differences would form us in non-identical ways, resulting in some small differences. These differences would ultimately affect the choices of me and my replica and consequently our preference would diverge. This, in turn, would lead to escalating environmental differences and increasingly different personalities or, if you prefer, souls. The resulting differences between me and my replica would be reflected in the way our atoms are put together, so we would no longer contain the exact same atoms. Nevertheless, there would probably be many striking similarities as well. There are examples of genetically identical twins that have grown up in very different environment, and still similarities have been extremely apparent.
What do I base this belief on? My main piece of evidence is that there does not seem to be any part of the personality that cannot be affected by brain injury. In my neuropsychology course I read about many patients with exotic brain injuries. A famous patient called HM, who is still alive, is unable to form any new memories. As a result he still thinks that he is 25 years old and he does not recognize the researchers who have visited him every day for several decades. Another older case is that of Phineas Gage who got a metal stick shot up through the frontal part of the brain. To everyone's amazement Gage did not die from the injury, however, according to his colleagues he was not the same after the injury. Following the injury he started swearing and behaved inappropriately to the extent that he lost his job. However, the most striking case that I can remember only vaguely is that of a responsible normal woman with three kids. Due to a tumor in her brain she suddenly underwent a radical personality change. Her behavior went from normative to completely reckless, and from being a good and faithful wife, she became extremely uninhibited and promiscuous…
One needs merely to take a look at a severe case of Alzheimer disease to see that material changes in the brain can change a person beyond recognition. Some would say that there is always something left, that even though Anna is now eating her own feces and hitting her children when they come to visit, she is still Anna, somewhere inside. I don't think so. Sure, she is still called Anna, and one can still recognize her appearance, but other than that Anna is not Anna anymore. The soul of Anna is very different from the soul Anna used to have before she got Alzheimer.
In sum, due to the fact that there seems to be no sacred part of the personality, nothing which cannot be affected by changes of a material nature. Due to this I do not believe that we have an immaterial soul. Normally I try to avoid the word altogether because of the confusion that arises, but this is my current thoughts on this issue. The discussion here has many important implications, for instance it should affect how to think about free will vs. determinism. I have written about that here.