Here is an article about the SSM-N-8 Regulus cruise missile, deployed between 1955 and 1964 by the U.S. Navy. Test missiles were equipped with landing gear and a parachute so they could take off, be recovered, and reused.
On 1959-06-08, the U.S Navy submarine USS Barbero launched a Regulus missile carrying 3000 pieces of mail aimed at Naval Station Mayport in Florida. The missile arrived, descended by parachute, and the mail was unpacked and taken to the post office in Jacksonville, Florida for delivery.
According to the Wikipedia article on rocket mail, U.S. Postmaster General Arthur Summerfield said: “This peacetime employment of a guided missile for the important and practical purpose of carrying mail, is the first known official use of missiles by any Post Office Department of any nation.” He proclaimed the event to be “of historic significance to the peoples of the entire world” and predicted that “before man reaches the moon, mail will be delivered within hours from New York to California, to Britain, to India or Australia by guided missiles. We stand on the threshold of rocket mail.”
Sixty-four years later, we’re still waiting for rocket mail.