What's the origin of 108 being a sacred number?

The number 108 is a sacred number in Buddhism, but in [other religions as well](http://en.wikipedia.org/wiki/108_(number)#Religion_and_the_arts) (Hinduism, Jainism). What exactly is the origin of 108 being a sacred number in Buddhism? Is there anything about it in the ancient scriptures? Did the Buddha say anything about it? Or is it more likely that this was incorporated from other older beliefs?