I certainly don't believe in a soul as any mainstream religion defines it. As said by others here, you see how brain damage changes a person drastically, so if the soul concept was true, they'd still be the same person, just with handicaps.
That said... we know the brain, which is essentially us, is a collection of electrical impulses at a basic level, and energy cannot be created or destroyed, it always exists in one form or another in potential....
Therefore, while we may not have a soul with memories, I'd like to think that we have got something akin to a soul in that being a life force. An energy that is a part of us and will exist still after we've gone.
If that can be classed as a soul, then yes. I believe in one.