I know sites like Facebook are now using REST services, but I am wondering of other applications that use REST and if there are specific situations when the use of REST is more
There are LOTS of REST interfaces out there: flickr, and Google's data APIs come to mind as two big examples.
REST is great for simple data interaction and stateless connections (similar to HTTP itself). SOAP is a common alternative, and is often used for more complex connections. REST is very popular these days and is a good place to start if you're just learning why you'd want to have a data interface. Designing REST interfaces is easy to learn and has low barriers to entry.