7Timer is a free to use graphical API mainly derived from the NOAA/NCEP-based numeric weather model, the Global Forecast System (GFS) that will display the forecast diagram for anywhere over the world.
Pokeapi is a free to use API that covers data based on Pokemon from the video game franchise. It has accessible data from all the Pokemon in one place.
The free Bored API helps you find things to do when you're bored. There are fields like the number of participants, activity type, and more that help you narrow down your results.
In summary, there are many free public API's available for everyone to use.