A whole-body transplant, or brain transplant, moves the brain of one being into the body of another. It is a procedure distinct from head transplant, which involves transferring the entire head to a new body, as opposed to the brain only. No technology currently exists to perform brain transplants.
Although many scientists would challenge the feasibility of this process, few would say that it is not eventually possible given current research into organ transplant and human cloning. Some bioethicists would argue that there are difficult moral problems involved in either harvesting a brain-dead body, especially one deliberately created using human cloning, or otherwise acquiring a body (say, of a criminal due to be executed for a crime, or an individual who is not dead but is soon to die of a brain-based illness).
Whole-body transplant is similar in some ways to the idea of downloading consciousness promoted by Marvin Minsky and others with a mechanistic view of natural intelligence and an optimistic outlook regarding artificial intelligence. It is also a goal of Raelism, a small cult based in Florida, France, and Quebec. However, while the 'downloaders' see the ultimate receptacle of the human brain as a repairable manufactured body made by robotics, the 'transplanters' see the ultimate receptable as a new body optimized for that brain by genetics and maybe proteomics.
It has been pointed out that the age of a body that a brain could be transplanted into should be sufficient - the adult sized brain could only fit into the skull of a body post 9-12 years old as that is when the head reaches adult size.
The procedure seems to be a far-off goal. However, it should be noted that human cloning itself seemed impossible a generation ago.
See also: human cloning, organ transplant, Raelism, robotics, I Will Fear No Evil