November 25, 2017 — Last week I explored the question "how many programming languages are there in the world?". My current estimate is between 5,000 and 25,000 active computer languages.
But perhaps the number is higher, if you include all active external web APIs.
Zapier lists over 750 APIs.
On GitHub user abhishekbanthia maintains a popular list of about 300 apis. Wikipedia has a small list of about 30 APIs.
My estimate is: between 2,000 and 25,000 active public facing web APIs.
My ad hoc estimates are based on checking the PLDB database, the datasets listed above, and additional web sources.