I am often asked for API examples. The problem for me was always pointing someone to business APIs without them having access to those APIs. Cameren Dolecheck came up with a post with a collection of public APIs solving this dilemma:

1. PokeAPI The largest media franchise of all time now has an easy way to get data on the 800+ Pokemon.
2. NASA API Space, the final frontier. Get data on astroids, galaxies, and more.
3. Open Food Facts A huge amount of data on food products from around the world.
4. TransLoc OpenAPI Get live data of public transportation of cities and college campuses.
5. Urban Dictionary API It’s amazing what slang people come up with.
6. Merriam-Webster Dictionary API For those that want real words’ definitions and synonyms.
7. Numbers API Interesting facts and trivia on numbers.
8. WeatherBit API Current and historical weather data.
9. US Government Data API A fairly big catch-all for dozens of United State data samples such as agriculture, health, and public safety.
10. Bible API The best selling book of all time. The greatest story ever told.

Beside this he points to two other great resources for public APIs:

You can find a huge list of public apis at this Github and an even grander list at RapidAPI.

If you are looking in how to design APIs or how they are built have a look at these sources.