Pirate Weather [via Hacker News] is a "Free, Open, and Documented Forecast API", which is to say that it tells you the weather, the way you want it, without having to directly access crude government-run or expensive commercial data sources. Contrary to its name, it legally repackages public data in a more useful form; the context is the imminent death of Dark Sky and its API, following its aquisition by Apple.
Weather forecasts are primarily determined using models run by government agencies, but the outputs aren't easy to use or in formats built for applications. To try to address this, I've put together a service (built on AWS Lambda) that reads public weather forecasts and serves it following the Dark Sky API style. It is not a reverse engineering of the API, since their implementation relies on radar forecasts for minutely results, as well as a few additional features.
Some quick links:
Get a weather forecast in the Dark Sky style: https://merrysky.net/
A simple weather forecast page: https://weather.pirateweather.net
For the technical blog describing the setup: https://docs.pirateweather.net