Zip Code Basics
Zip Code Look-up (U.S. Postal Service). Search by address, city, or business name to find zip codes. If found, the appropriate ZIP+4 Code will be returned. Can also find city name by zip code. Includes a link to the Postal Service's Zip Code FAQs.
What is a Zip Code Tabulation Area? (Census Bureau).
MABLE/Geocorr2K: Geographic Correspondence Engine with Census 2010 Geography--Relate U.S.Counties, Zip Codes, Census Tracts, Congressional Districts, etc.
To obtain a list of all Zip Codes within a state, county, or place (i.e. city), follow the directions provided at the end of the Census Bureau's Zip Code Statistics page.
Some companies provide free samples of data. (They hope to inspire you to purchase their products). Examples include ZipFind and ZipCodeDownload, which offer free searches to find the distance between Zip Codes and/or Zip Codes within a certain radius of another Zip Code. Another example is Zip Codes in a County from Melissa Data.
The ZIP Code Resources Page lists other tools and includes a discussion about problems encountered when using Zip Codes to represent geographic areas.