Do I believe in reincarnation in that the atoms and molecules that make up my body will go on to be apart of something else? Sure.
Do I believe in reincarnation in that my "soul" will be reborn again? Nope.
I'll paraphrase what Sam Harris said. Your brain is a apart of what makes up you. Neurology is the science of the brain, and it has shown us that when you damage part of the brain you damage areas that deal with certain things. Some damage can make a person not remember faces, some damage can make a person forget to speak. You can even damage the brain to a point where it starts to process things differently, you start to act differently than you used to, and suddenly "you" are the same person anymore. But somehow, if you damage the entire thing, your "soul" will lift off of the brain and you will be able to remember how to speak English and remember everything you ever did.
I'll admit, reincarnation is an interesting idea, but, aside from anecdotal evidence, there is no scientific proof that it actually happens. To think it does is nothing more than wishful thinking, imho. I try to live my life, the only one that I know for a fact I will ever have, to the fullest I can possibly can.