The Census Bureau does not publish data by Zip Code. Zip Codes are mail delivery codes created at and for the convenience of the U.S. Postal Service. Zip Codes are not consistent geographic units and the Census Bureau has to have consistency in a geographic unit in order to create meaningful statistics.
However, the Census Bureau did create "Zip Code Tabulation Areas" for Census 2000 which approximate real Zip Codes. Data from Census 2010 will eventually be available at the ZCTA level too, but the American Community Survey will not. As the American Community Survey is now the only source of nationwide socio-economic statistics for small geographic areas, this means users who need data organized by Zip Code will need to look elsewhere.