Perhaps not as far off as you may think. It would be a surprisingly simple, if dangerous, procedure to transplant the brain and spine into another body. The main problem, however, is just retaining consciousness, but I believe that can be done by using sterile environment, moving the entire skull and spine with brain hooked to special IV set, and cutting out the brain and spinal cord and planting them into the new body. More than likely, it is not a surgery a human could directly participate in.
I feel that once that is done, the transhumanism we see in scifi will pretty much have arrived, as a sort of singularity (singularity as in where previous generations will be unable to comprehend the new technology) The brain and spine transplant would need some hefty amounts of genetic engineering and computer engineering just to be able to use the new body.