7Timer!
7Timer! is a free to use web based weather forecast API derived from the NOAA/NCEP based numeric weather model, the Global Forecast System.
Link to 7Timer! API SiteCocktail Database
The Cocktail DB is a free API used to search a database of cocktails, ingredients and cocktail related thumbnails.
Link to TheCocktailDB API SiteZippopotam.us
Zippopotam.us is a free postal code database that provides the names and geolocation of an area based on their postal code.
Link to Zippopotam.us API SiteSummary
There are a seemingly infinite number of free APIs that are available for an exteremly wide range of topics. There are even APIs for lists of APIs.