It is possible to find ZIP codes through a Google search. A Google search can provide you with a ZIP code if the town name is known. Conversely, a town name can be provided if the ZIP code is known.
In order to search for a ZIP code, use a search term such as "ZIP code for [insert town name, state]". This brings up a result page. Located at the top of the result page is list of all relevant ZIP codes for the area that was searched for. The same process can be used to derive a town or area name based on a known ZIP code.