Unlike telepathy and psychokinesis, OBEs and NDEs are so common and striking that no one (that I know of) denies their existence; the only question is one of interpretation. The NY Times has reported that OBEs can be "induced by delivering mild electric current to specific spots in the brain," and therefore concludes that it the experience is the result of the "brain's attempt to make sense of conflicting information." You can see a video of this here. Susan Blackmore, a leading researcher and philosopher on OBEs and NDEs, basically concludes the same, but puts a little pseudo-Buddhist twist on her reductionist theory.
However, before we get to the evidence against the "brain-only hypothesis," I want to point out the logical flaw in this argument. It may be true that certain experiences can be induced under certain conditions but that does not mean that all such experiences, or something similar to it, must share the same explanation. In this case, OBEs occur in many different conditions- in extreme stress and in sleep, with volition or involuntarily, in meditation and hypnosis or during mania and drug use. Bruce Greyson, a foremost expert on NDEs, is quoted as saying "We cannot assume from the fact that electrical stimulation of the brain can induce OBE-like illusions that all OBEs are therefore illusions." Also see here. This is a common mistake that skeptics of the paranormal make; if they can come up with one explanation during one condition they generalize it to all such paranormal experiences. We will come back to this point in later posts.
There are two main pieces of evidence that demonstrate that an OBE, at least sometimes, is not a hallucination but an experience where the self leaves the body.
"As her physician was closing the incision, Sarah's heart stopped beating...But the emergency was over in a minute for it took no more time than that for the anesthesiologist to defibrillate her...She had some thing else to show that amazed her and the rest of the surgery team as well - a clear, detailed memory of the frantic conversation of the surgeons and nurses during the cardiac arrest; the OR layout; the scribbles on the surgery schedule board in the hall outside; the covering of the sheets covering the operating table; the hairstyle of the head scrub nurse; the names of the surgeons in the doctors' lounge down the corridor who were waiting for her case to be concluded; and even the trivial fact that her anesthesiologist that day was wearing unmatched socks. All this she knew even though she had been fully anesthetized and unconscious during the surgery and the cardiac arrest. But what made Sarah's vision even more momentous was the fact that, since birth, she had been blind (Larry Dossey, Recovering the Soul, pg. 17-18)."
Kenneth Ring in Mindsight have reported dozens of cases where the blind have some sort of sight during OBEs or NDEs. Regardless of whether these visions were independently verified by others, it is still quite unexpected for a blind person to see during an OBE if it were just a hallucination. From my limited research it seems that blind people on psychedelic drugs do not experience visual hallucinations.
The second type of evidence is when an OBEr sees something that at their body's position would be impossible to see. I first heard of this from a friend about a friend who trained himself to have an OBE before falling asleep. To check whether he was really leaving his body or it was just a hallucination, he placed a playing card on the other side of the room without looking at it. During the OBE he would travel to the other side of the room and look at the card. When he woke up he would check whether he could "guess" the right card. He could. These homemade experiments went on until a well-known Kabbalist (you could guess who) told him to stop.
Charles Tart had the same idea and here is an account of one such experiment with Miss Z: "Each labatory night, after the subject was lying in bed, the physiological recordings were running satisfactorily, and she was ready to got sleep, I went into my office down the hall, opened up a table of random numbers at random...I the slipped it into an opaque folder, entered the subjects room, and slipped the piece of paper onto the shelf without at anytime exposing it to the subject. This now provided a target which would be clearly visible to anyone whose eyes were located approximately six and a half feet off the floor or higher, but was otherwise not visible to the subject. The subject was instructed to sleep well, to try and have an OBE...She was also told that if she floated high enough read the five-digit number, she should memorize it and wakw up immeidately afterwards to tell me what it was...The number 25132 was indeed the correct target number near the cieling above her head...the odds of guessing a five-digit number by chance alone on one try are a hundred thousand to one (The End of Materialism, pgs. 202-203)."
It seems that the only other plausible explanation of this story is telepathy so take your pick...