The United States Postal Service began to assign two digit zone numbers to various parts of large cities in 1943. After 1944 they began to assign three digit area numbers to all parts of the United States, but this was originally for internal purposes only.
It was not until 1963 that the Postal Service began a full throttle effort to get the American public to adopt the zip code system and it wasn't until 1967 that the Postal Service required all second and third class mail to have a zip code. The zip code system allowed the Postal Service to put most first classs mail on airplanes and to use trucks for most of the rest. After 1963, the Postal Service canceled or allowed to lapse, all of its Mail contracts with the railroad companies. Railroads had been losing money on passenger trains, since 1925, but these loses were mitigated by the revenue they got from moving mail and express (small packages) traffic. The Railroad Express Agency was facing serious problems during the 1960s as UPS and the Post Office's own Parcel Post service cut deeply into its revenues. With the zip code system and the cancellation of most Mail contracts, the final prop that was supporting the money losing passenger trains in the United States was kicked away. That led to a sharp increase in passenger train cancellations during the late 1960s and the creation of Amtrak in 1971.
Essentially, every post office in the United States has its own zip code. The specific streets served by each post office was determined before the zip code system was even implemented. The following web site will provide more information on these technical details.
http://www.zipboundary.com/zipcode_history.html
This web site also shows one of the corny Public Service Announcements, the Postal Service used to promote the use of zip codes, circa 1963.

Can you still use tpc codes to increase speed when sending a letter?