There is one place in America that still gets its mail delivered by mule. Located deep within the Grand Canyon, the village of Supai is billed as the country's most remote town. They rely on the mules and helicopters for any deliveries, and it turns out that mules are much more dependable and much less expensive than the whirly birds. The journey down the canyon takes about 3 hours. They have a special postmark for their mail. It is something of a tourist attraction, a boon to the residents since most of their economy is based on tourism. I know it's on my list if I ever get to the Grand Canyon.
P.S. Thanks to member Kimberly AH for her tweet to the Smithsonian article.