There's a lot of evidence surrounding NDEs and OBEs. Generally, if researchers bother to read through it there's a consensus that both are valid phenomena which traditional science cannot as yet explain.
One take is that consciousness is not restricted to the physical body. This take explains a few other things too but I wont go into it here. There have been studies done as User76 described, and there have been retrospective studies done primarily on cardiac patients who were asked to describe the procedures they underwent and so on.
Generally it's dismissed because it doesn't sit well with current generally held beliefs about how the body and the mind work.
This is the sort of stuff which currently has me
stumped
Twenty Inch has the book at the minute and Marinyork has been helping my line of thought. I'd be very interested to know what you think Kirstie, if you have time to read it.