The Life of David Brainerd by Jonathan Edwards is probably one of the most influential missionary biographies ever written. Even though he died of Tuberculosis at the age of 29, his account of his relatively short life as a missionary to the American Indians has become a missionary classic. This was a significant book for both William Carey and Jim Elliot.
You can get the free audio book from Christian Audio. You may need to register and you will need to use the coupon code OCT2007 when you get to the checkout.