It may sound a bit nuts at first, but its actually a far more central aspect to the whole discussion than you may expect. The arabic numeral system is one of the more profound mathematical leaps forward in history. As an amusing exercise, try brushing up on roman numerals and then attempting to write some medium to large numbers. You'll find there is no general correlation to the length of a number string and the size of the number. Its even more unwieldy if one attempts to do arithmetic on these objects. But still the question of "why ten?" While it is certainly possible to formulate a similar system in a different base consider two further points; the ease with which we can teach arithmetic to children, and the linguistic considerations of a culture.

About the first point; every child comes equipped with a built in abacus in base ten. Its this biological fact that allows for us to teach basic arithmetic at such a young age. Early exposure is the first step in getting these things to become automatic and finger counting for a very young child is a highly important tool. To be fair, the linked article has an alternative suggestion to this which uses sections of fingers instead of fingers to count. I would argue that in the mind of a child it is a far easier and less subtle idea to count with whole fingers instead of sections. I'd also posit that the younger a child the harder it is to explain a concept like sections of fingers. Whole finger counting is so intuitive that I'd bet there are kids out there that didn't even need to have it shown to them.

As for the second point; there is a really funny correlation between the cultural development of our language and the way we think about numbers. I read a book a few years ago on the history of mathematics and in it the author discusses the findings of some historical anthropologists. They studied various indigenous peoples who had remained relatively isolated from the rest of the world. Their findings showed a surprising correlation between the warmth of the climate and the sizes of numbers they had words for. Cultures in very cold places would often only have words for 'one' 'two' and 'many' while people in warmer climates could often go as high as twenty. Their conclusion was that there was a direct correlation on the number of digits available to count with and the sophistication of a peoples counting system. If you wear gloves and boots all the time its kinda hard to finger count. Conversely, if you have sandals on, there's whole 'nother row of ten piggies to utilize.