I don't believe that souls exist. Like YV, I cannot prove that they do not exist, but the only reason I would have to think that they do is that it is a nice, happy idea.
I frequently argue with people who tell me the soul is "life energy" which takes on other forms after death. No one has ever offered to tell me what "life energy" is, accusing me of being close minded and fleeing to the safety of the "not everything in the universe is known to science" argument. As a result, I have to shoulder the burden of proof, which is extremely frustrating as I am not the one trying to prove an idea.
Of course, our bodies do contain energy - chemical and thermal energy. The former is consumed by other organisms after we die, and the latter dissipates as heat.
I know people like to use the "absence of evidence is not evidence of absence" counter. However, such an argument becomes absurd when one argues for any random, unprovable idea. I could argue that the universe is floating in the nose of a cosmic llama and argue that no one can disprove me.
To quote Richard Dawkins:
"Let us be open minded, but not so open minded that our brains fall out."
Wanting to believe something means one needs extra skepticism, as the desire for something to be true can cloud one's reason.
L'enfer, c'est les autres. -Jean-Paul Sartre