The JSON Placeholder is a service that provides you with fake online REST APIs for testing and prototyping. It is a go-to API for developers. It is free to use, and serves around 2 billion requests each month.
Open Weather Map is a free service that provides you with easy access to their data via their API. They have a variety of data collections to choose from depending on the needs of your project.
While most of Google's APIs require you to pay, the Translate API provides free translations for 100+ languages, and up to 500k characters per month.
A simple google search will render a plethora of free APIs for developers to use. While I've only listed three here, there exist an endless variety of APIs to choose from on the internet.