We count in base 10 because we have 10 fingers. 10 is not a particularly good number to use every day: it divides only into 2 and 5, so many everyday operations (such as splitting something into a small number of equal parts) are just painful with a decimal numbering system. Of the remaining divisors – 3, 4, 6, 7, 8 and 9 – all but two yield nasty infinite decimal expansions (because 3, 6, 7 and 9 factor into primes that don't appear in the prime factorization of 10), 3 being the most painful one since it appears in nature so much.
I wish we had 12 fingers. 12 is a number that is far superior to the number 10. It divides evenly into 2, 3, 4 and 6 parts. Dividing into 5, 7, 10 and 11 still produces infinite expansions, but who needs to divide into 5 in nature anyway.
A friend of mine noticed that if the additional two fingers were opposing, like our thumbs, our hands would be infinitely more agile. Just think about the sorts of manipulation (and hence the sorts of tools) we would be capable of with two thumbs at each hand!