The base of ten is the most natural oneIt probably just seems that way because we're used to it. At some point when designing a system of numbers, 10 was a convenient answer to the question of how many digits to use. This doesn't mean it has a neurological basis.
I searched the Web a little bit for research pointing to a neurological basis for decimal. I didn't find it, but I did find this article on the brain's handling of numbers: http://arstechnica.com/science/news/2007/01/6661.ars
I see the base 10 as the only really important base to us humans (machines may have different preferences...)
If communication is ever established with non-human intelligences, it will be important to move beyond speciesism. When aliens finally land, or AI awakens, we should be able to say "Welcome. All your base are okay with us."