Datamuse
Word-finding query engine
Drupal.org.
Drupal.org API is a free Open Source Projects API that requires no API key, is served over HTTPS and has unconfirmed CORS support.

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Word-finding query engine
Evil Insults
Yes. The Drupal.org API is listed in the Open Source Projects category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
No. The Drupal.org API requires no authentication, so you can start making requests without signing up.
CORS support for the Drupal.org API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The Drupal.org API is served over HTTPS, so it's safe to use in production.