Re: why does the right half of the brain, control the left side of the body?

The cross connection of many areas of the central and peripheral nervous 
systems is based on "decussations" -- neurons which cross the midline from 
their point of origination.  The sensory and motor systems cross at 
different points in the lower brainstem (the sensory and "pyramidal" 
decussations in the rostral and caudal medulla oblongata respectively. 
There are also decussations in the brain itself where sensory 
representations from one side of a sensory field are mapped onto the other 
brain hemisphere.  There is an excellent interactive anatomy guide to the 
CNS which describes the locations and paths of some of these crossing 
points at 
http://www.anatomy.wisc.edu/Bs97/text/BS/
contents.htm

But as to the "why" that has been a poorly examined but often asked 
question.  One possibility (not examined but raised during a conference) 
was that adding the extra length of neuron allowed a more precise timing 
for action potential arrival for very long axons, or when you may be 
getting input from neurons of multiple lengths.  The other possibility is 
derived from some neuronal mutants (and I apologize for not having the 
exact referents available -- if you email me I will try and find them -- I 
believe they were developed at Stanford) -- these vertebrate mutants 
developed normally, but lacked decussations.  The only effect?  When they 
were picked up, they split in half and fell apart.  So perhaps there is a 
structural aspect and decussations help bind the bicameral central nervous 
system together.