Zipcode shape database as lat/long data

@Brandon, ZIP codes aren't polygons but you could use ZCTA shapefiles from the Census.

ZCTAs are polygons and will give you a serviceable map as long as you don't zoom in too close. Here is a short summary:

ZIP Code tabulation areas (ZCTAs) are geographic approximations of U.S. Postal Service (USPS) 5-digit ZIP Code service areas that the Census Bureau uses to present statistical data from censuses and surveys. The Census Bureau defines ZCTAs by allocating each census block that contains addresses to a single ZIP Code tabulation area, usually to the ZCTA that reflects the most frequently occurring ZIP Code for the addresses within that block. Blocks that do not contain addresses but are completely surrounded by a single ZIP Code tabulation area (enclaves) are assigned to the surrounding ZCTA; those surrounded by multiple ZCTAs are added to a single ZCTA based on the longest shared border. The Census Bureau identifies 5-digit ZIP Code tabulation areas using a 5-character numeric code that represents the most frequently occurring USPS ZIP Code within that ZCTA. This code may contain leading zeros.

Here is the detailed Census documentation.

This is a link to the National States Geographic Information Council's zip code database. It should have what you need.

https://catalog.data.gov/dataset/zip-codes-zipcodes

If it doesn't this site has a paid zip code database (which is free for personal use)

https://www.unitedstateszipcodes.org/zip-code-database/

Keep in mind though, a large part of the country actually has no zip code (I'm from the northeast and had no idea for a long time this was true). But, areas of the west where there are no people (mountains, deserts, etc.) have no zip code.