DSDR KB:

You are correct. With NHGIS you can get data for all census tracts in the nation in a single request, but to get the equivalent data for zip codes would require 30,000+ requests. The best solution for you is to use the Download Center at the Census Bureau. You can get a limited number of tables for all zip codes in a single request. The limited number of tables is pretty generous - 50.

If you are interested in a smaller number of zip codes - say all zip codes in a state - you can use the American Factfinder interface. In that case, select 5-Digit ZIP Code Tabulation Area (ZCTA). You will be directed to select a 3-Digit ZCTA and can select "All" which gives you all the 5-digit zip codes in that 3-digit area. You can repeat this over and over until you have reached the limit of 7,000 geographic areas.