The cartoon show "Futurama" plays with this idea by having a large number of celebrities' heads preserved in jars. The result is a being that is just like he or she was before the process. (Which allows the writers to make jokes about current celebrities while still placing the show a thousand years in the future.)
Modern research in brain physiology totally rejects this idea. As I understand it, scientists have found out that the brain is dramatically influenced by the hormones that are released by our entire body. Of course, a moment's reflection should point out that a disembodied head would no longer have either estrogen or testosterone being released into the brain---which means that probably it would cease to feel any sexual desire. In addition, without an intestinal tract, hunger would no longer exist.
Beyond these obvious issues, there would be a great many other things missing too. For example, a large part of the exhilaration we feel in life comes from the physical sensations we have when doing things like moving with speed, grace and dexterity. It is to mimic this experience that people like to ride on things like roller coasters, for example.
Take a good look at this photo. It gives me a feeling of vertigo, which again involves the release of hormones into the bloodstream, which influences the way our minds operate.
The experiences I am having in trying to deal with my PTSD directly relate to the way the brain and body interact. One of the worst elements of PTSD is having "flashbacks". These are dreadful experiences where I feel all the emotions that I felt when I was experiencing absolute and utter terror as a child. The emotion registers itself in physiological responses: I am drenched with sweat, my heart races, etc. My body is creating the hormonal response that evolution has prepared for the situation of having a tiger jump out of the bushes, yet I am safe at home with nothing but memories of my childhood threatening me. Even when I'm not having a full-fledged flashback, my recent experiences have consisted of feeling very sad and a smaller amount of anxiety for most of the day for a couple weeks---which is tremendously exhausting.