I use the following 3 APIs for teaching purpose:
* Spotify search https://developer.spotify.com/technologies/web-api/search/
* Everything in Iceland from buses to lottery including earthquake http://docs.apis.is/
* Football data (european football results, rankings…) http://www.football-data.org/
Also, similarly to Iceland, some cities open some of their data through APIs as part of an opendata initiative. Not all do require an API key, and some present interesting data in a nice way.