If you need commercial grade, consider this: http://greatdata.com. If you do not need this level of quality, here is a list of some other sources w/ pros & cons (it's worth reading just to understand the differences between zip, zcta, usps, census, etc. versions of the data).
ps -
you said 'entire world' but your other responses and the term 'zip code' itself seem to imply primarily US. The above link goes beyond US but not the entire world.
Regarding the Google API mentioned already, please be aware of Google's TOS. Specifically: "Note: the Geocoding API may only be used in conjunction with a Google map; geocoding results without displaying them on a map is prohibited."
I am an employee for greatdata.