In the olden days, one could address an envelope as follows:
Legally, the postal service is under the obligation to deliver a piece of mail whenever possible. In the old days, one's carriers knew exactly where everybody lived, and the envelope would get through.
Here's another example:
[above images from postmarks.org]
Postal zones were introduced in larger areas in 1943. For instance, in New York, New York, postal zones generally progressed from the south of Manhattan north -- zones 1 to 40. Furthermore, in The Bronx were New York zones 51 to 75. Here are maps of Manhattan and Bronx ZIP codes.
[Aside: Mail processing for the Bronx was handled in New York until Congress authorized the institution of an independent Bronx post office and processing center. Approval occurred in August 1962. (The author has been unable to ascertain the exact date The Bronx became an independent post office.) Ironically, processing at the Bronx GPO might be moved back to Manhattan at the end of this year.]
Once postal zones were implemented, here is how people could address their mail:
The 1960s heralded the advent of ZIP (Zone Improvement Plan) codes. From inventors.about.com: "By July 1963, a five-digit code had been assigned to every address throughout the country. The first digit designated a broad geographical area of the United States, ranging from zero for the Northeast to nine for the far West. This was followed by two digits that more closely pinpointed population concentrations and those sectional centers accessible to common transportation networks. The final two digits designated small post offices or postal zones in larger zoned cities."
Most post office signs show their modern ZIP codes. But I discovered two Boston post offices whose signage shows their old postal code designations: the Grove Hall Station and Belmont Branch.
Boston 21 correlated with Grove Hall in Dorchester, and became ZIP code 02121:
The Boston suburb of Belmont was the 78 zone of Boston, and now has the ZIP code 02478: