Here's a very partial list of service providers that use a REST API. Note that some of them also support a WSDL (Web Services) API, in addition, so you can pick which to use; but in most cases, when both alternatives are available, REST calls are easier to create, the results are easier to parse and use, and it's also less resource-heavy on your system.
So without further ado, some REST services:
- The Google Glass API, known as "Mirror API", is a pure REST API. Here is an excellent video talk about this API. (The actual API discussion starts after 16 minutes or so.)
- Twitter has a REST API (in fact, this was their original API and, so far as I can tell, it's still the main API used by Twitter application developers),
- Amazon.com offer several REST services, e.g., for their S3 storage solution,
- Atom is a RESTful alternative to RSS,
- Tesla Model S uses an (undocumented) REST API between the car systems and its Android/iOS apps.
(This is far from an exhaustive list.)