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. Most ethicists would argue that there are extreme moral difficulties 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 religion 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. Both goals are often derided as insane or unethical by religious and social leaders, who point deep to the disruption and inequality immortality of any sort is likely to cause.
Others point out that the age of a body a brain could be transplanted into is limited - 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 issue seems to be somewhat far off. However, it's important to note that human cloning itself seemed far off a generation ago. There have been many successful head transplants performed on monkeys by Dr. Robert White of Case Western University, and he announced in 1984 that he felt his techniques were suitably developed to work on humans.
See also: human cloning, organ transplant, Raelism, robotics