Nikolai, Alaska
The website Gawker has gone through the Ashley-Madison information dump, and they found that only three zip codes in the entire U.S. did not have any Ashley-Madison users on record. Three!
Two of those zip codes are in Alaska: Nikolai and Perryville. Populations of 94 and 113 respectively. Polvadera, New Mexico (population 269) was also on the list.
There are approximately 43,191 zip codes in the United States.