I'm not usually one to pick on Buddhism, I generally think it's pretty cool as far as religions go. A lot of what Buddhism has known about the mind for centuries is being confirmed by science at every turn. However, there are a few things that I don't think mesh very well. Namely, the concept of oneness seems to contradict the concept of the soul.
Alright, first a little background. The one truth, as far as I can tell, is oneness. Separation is an illusion created by the limitations of consciousness. That is, what makes me separate from everything else is the fact that my mind does not have access to everything. If my mind had access to everything in your mind, all of your memories, all of your experiences, all of your thoughts. If I could think with your mind, and you had the same access to my own mind, then we would cease to be two separate people. The idea that I am separate from anything else is basically an illusion of my own ignorance. "I" am, because of what I don't know.
Furthermore, the physical and chemical separation between things is a similar illusion. In "cycle of life" fashion, all things are connected. I am a sack of chemical reactions, but I also depend upon chemical reactions which occur outside of my body. The line where "my" chemical reactions begin and those of "not me" end is rather blurry if it exists at all. It seems that once again, separateness is an illusion that our minds cook up to make sense of things. That is, separateness exists in my mind, not in the "real" world.
So if mental separateness is an illusion, and physical separateness is an illusion, what about spiritually? The soul is obviously a concept of separation. What separates "my soul" from "your soul" is that mine is not yours. They are two separate souls. Now, it may be the case that the spiritual world is a different sort of thing from the mental and physical worlds... but that would seem like special pleading. It seems to me that a doctrine which focuses on oneness and upon the illusion of separation, that they would also stress the concept of spiritual oneness. Yet, there is the soul, and it reincarnates until it reaches enlightenment and is removed from the cycle of reincarnation. But for a soul to be reincarnated and removed from that same cycle, it must be a separate thing from all the other souls. But that doesn't seem right to me. Just like the concept of mental and physical separation are useful fictions, wouldn't the soul be a similar useful fiction? Why wouldn't it be?
Now, it's also possible that I'm terribly misrepresenting Buddhism on this one. I'm limited by what I have read and my interpretations of those readings. However, the concept of oneness makes intuitive sense to me, and the soul makes intuitive sense to a lot of people... but the implications of the two do not mesh well. Is there perhaps a resolution that I'm not seeing? or have I just reaching enlightenment? :P
In Buddhism, there is no soul or self. This is known as the doctrine of anatta. Another important doctrine is "dependent origination". This states that everything is an effect of pre-existing causes and is in turn a cause of other effects. Rebirth is an effect of causes in previous lives. There is no soul jumping from an old body to a new one. The incorrect belief that we are independent entities is one of the primary causes of suffering in the Buddhist view of things. The book "A Profound Mind" by the Dalai Lama has a good explanation of this.
It seems then that the Buddhist concept of reincarnation is more than a bit confusing. What point is there to even using that term when it is merely a string of consciousness? I get the concept that the consciousness of this generation flows into the next. However, how does one manage to remove themselves from this cycle? Is it merely the removal from the cycle of suffering? If that's the case, then that's probably about as unproductive a phrasing as the "observer" in quantum mechanics.
Additionally, it seems to me like Nirvana, at that point, becomes meaningless for the individual and could never exist unless all were in Nirvana.
I've known a handful of people who claimed to be Buddhist, and they all seem to be of the opinion that the soul exists and that reincarnation is exactly as pop culture would have it. Perhaps these are simply new-agers who meditate and have therefore adopted that label.
One removes oneself from the cycle of rebirth by realizing the true nature of reality and no longer trying to grasp what is illusory. Some modern Buddhists, such as Stephen Batchelor, author of Confessions of a Buddhist Atheist, have done away with the belief in rebirth. I think that perhaps many Buddhists, even many who were born into Buddhist cultures, have a poor grasp of the philisophical foundation of Buddhism. A good scholarly discussion of the concept of anatta is "Central Philosophy of Buddhism" by T.R.V. Murti.