The Cold War was an interesting time for America. Any idea which gave the U.S. an edge over the Soviet Union, real or perceived, tangible or psychological, was considered a viable field of study. This spirit of innovation as many benefits as it did questionable plans. For example, as the the U.S. planned to put a man on the moon, the U.S. had been planning to nuke the moon for at least a decade. The biggest outcome of the crazy innovation of the Cold War has to be "I can't believe they tried something so crazy" stories on the Internet, like the one you're currently reading.
In 1959, the Navy submarine Barbero had a Post Office branch onboard. Before leaving Norfolk, the office took on 3,000 postal covers (envelopes with special stamps, all cancelled, designed especially to be collectors items) addressed to government figures, among them President Dwight D. Eisenhower.
The Barbero was also loaded with a special Regulus cruise missile. Its nuclear warhead was removed and replaced with two post office mail containers. The target was the Naval Auxiliary Air Station at Mayport. 22 minutes after launch, the Regulus hit its target.
By this time, air mail allowed for mail to cross the ocean in a day, so the need for such high speed, costly, and non-reusable delivery services were not really destined for widespread use. In a nod to the idea of missile mail, Rocket Mail — one of the earliest major free email services on the Internet — before being acquired by Yahoo! in 1997.