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 many examples out there. GData and the Atom Pub Protocol are probably the finest. Twitter seems to have a nice REST API also. Amazon's S3 service is also quite "RESTful". Unfortunately, many services that claim to be RESTful violate the very core priciples of REST as laid out by Roy Fielding in his dissertation that described the REST architectural style.
REST is an architectural style, not a set in defined standard or implementation. This makes it more difficult to say what is and isn't a REST service, that's why you'll often hear "RESTful".
REST can be a great (and simple) alternative to SOAP, XMLRPC, and in some cases things like DCOM and CORBA. It can be a very simple way to facilitate basic distributed computing and a simple way to expose an API... especially due to the face that it integrates so nicely into the ubiquitous HTTP.