The New York Times Developer Network.
New York Times API is a free News API that requires apiKey authentication, is served over HTTPS and has unconfirmed CORS support.

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Yes. The New York Times API is listed in the News 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.
Yes. The New York Times API uses apiKey authentication, so you need to register for credentials before making requests.
CORS support for the New York Times API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The New York Times API is served over HTTPS, so it's safe to use in production.