When did the US postal service begin using zip codes?

1963.

1963: ZIP Codes are introduced. ZIP Codes are five-digit numbers that enable mail to be sorted faster. Use of the code was not mandatory on any mail at first.


http://www.zip-codes.com/united_states_zip_codes_timeline.asp


Before that we had "zones," two-digit numbers that pertained to a given area:

1943: The United States Post Office Department divides cities into zones. This was a precursor to the Zoning Improvement Plan Codes, or ZIP Codes.


In some if not all areas, the zones wound up as the last two digits of the new ZIP codes.