An api for accessing reddit information. Supports CORS. Doesn't require auth. Great for learning new frontend frameworks.
https://www.reddit.com/dev/api/
Similar to reddit, but different. Hacker News has posts, comments, and voting. You can use a firebase client for real time updates. Supports CORS.
https://github.com/HackerNews/API
All sorts of information about github repos, including issues. It can be used for learning new frontend frameworks.
https://developer.github.com/v3/
Upload and browse images. It can be used similarly to s3, limited to images, but it's free and fast.
https://api.imgur.com/endpoints
Lots of information about movies. You can create some cool movie listing sites with it.
https://www.themoviedb.org/documentation/api
Get your public ip and related info.
Create and read gists. It can be used to store arbitrary text. Supports CORS. It deserves a special mention.
https://developer.github.com/v3/gists/
Lots of starwars info.
Building a pokédex is fun and nostalgic, and you can do much more with this free api.
There are many sites like it, but this is the first result on google. It allows accessing web resources without getting cross origin errors. For example, you could use it to access this lorem ipsum text file. Sometimes the site crashes, so don't use it for anything too critical.