Purely in theory, would it be possible to transplant a human brain
from 1 person to an other assuming all the obvious issues like blood
type, tissue structure, etc. are a match??

Dear "I Wanna Know", 

Thank you for a very fascinating question - there's no place like here
to ask questions that have been bugging us for years.

As you probably know, brain transplant has not been tried yet (except
for fiction).

The most advanced, and highly controversial, experiment in the
direction of making Frankenstein a "reality" was conducted in 1970 by
Professor Robert White, from Case Western University Cleveland Ohio,
who managed to transplant a monkey's head into another monkey's body.
The transplanted monkey lived for some time after the operation (3).
That doesn't mean that the operation is possible, or that the
scientific community validates that as a "brain transplant". A
professor from the Open University UK said, that except for the
ethical problems, "All you're doing is keeping a severed head alive in
terms of the circulation from another animal. It's not connected in
any nervous sense." (3).

Except for White, there are other advancements. Scientists have
managed to transplant human neural stem cells in mice, which could be
used to handle conditions such as Alzheimer’s disease and Parkinson
(1). There have been experiments in transplanting tissue into the
brains of patients with certain neuro-degenerative diseases to try and
reverse the cell death (4).

A partial answer to this question could be found here
http://www.axel-and-alice.com/ddcl/ddca/ddca0131.html (5).

In other words, although there is no conclusive answer to your
question, it seems that technical advancement might bring about a
possibility of a head transplant. However, our brain is more than what
is in our head - it is attached to the nervous system and in fact
controls the whole body.

Sources
=======
(1) Susan Aldridge, PhD, "Brain transplant advance", Health and Age,
http://www.healthandage.com/Home/gid1=396 (Quoting a research
published in NeuroReport May 2001).

(2) Huma Q. Rana, "The Modern Day Brain Transplant: An End to
Parkinsonism?", Bryn Mawr College,
http://serendip.brynmawr.edu/bb/neuro/neuro01/web2/Rana.html

(3) "Frankenstein fears after head transplant" BBC News, Friday, 6
April, 2001, 10:59 GMT 11:59 UK

(4) David L Evens (devens@uoguelph.ca), "Re: news story: retarded girl
gets partial brain transplant; improves brain function",
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&selm=485r5m%24i97%40ccshst05.cs.uoguelph.ca

(5) Axel and Alice, "Do you think it will be possible one day to have
a brain transplant? "
http://www.axel-and-alice.com/ddcl/ddca/ddca0131.html.

I hope this answers your question. I performed a search on Google for
"brain transplant" and the words possible or possiblity. If you need
any clarifications on this answer, please let me know. I'd be pleased
to clarify my answer before you rate it.

Thank you for your answer Political Guru. 
The question occured to me after watching a show about transplanting a
hand from a recently deceased human to a man who in some manner had
lost his own hand.
After discovering this medium, I remembered that the issue had been
nagging me although I can't recall exactly why anymore.

Thank you again for taking to the time to indulge me.

connecting it so it would survive for at least a while is not a huge
technical challenge; meaning, hooking up the arteries and veins. The
body could only survive unsupported if it were also possible to
connect cranial nerves and spinal cord. The ability to do so
successfully is nowhere in sight so far. So basically, you'd have a
brain with no ability to control any part of the body at all, so it
would be no different from a brain being kept alive, in some way, in a
bowl.