Where can you find the enthalpy and Gibbs free energy of formation and entropy of compounds either as a data file or web API? Technically, I only need two since I can figure out the other one from two of them.
NIST webbook does have a lot of data, though they are not in any kind of an API form as far as I know.
NIST is the best place to turn for lots of data. However, more easily parsed, smaller datasets are available in a couple of other locations.
Rhas thermochemical data for a variety of species, mostly inorganic. Their database is referenced back to the chemical literature. See an answer I gave to an old question for an example of how to use it.
Robert Alberty's Mathematica package for biochemical thermodynamics has a lot of built in thermochemical data for common biochemical compounds -- relative to a biochemical standard state of constant pH.
Water-specific databases. In case you're only interested in water, ice, and steam, there are Excel plugins that let you get thermochemical data by calling functions inside Excel.
There appears to be a Python library called thermopy which contains a
burcat()module in which some thermochemical property data lives. I haven't tried it out though.
The database in that python module seems to be this one.
For biochemical reaction systems, there is also eQuilibrator which has a web interface.
This has proved extremely valuable (at least for me) and I think that others can also benefit from this.