Can you suggest some good example of some real-world and really well-done REST web api?
Amazon's REST API and Google's Search REST API are both good examples. eBay and PayPal also offer RESTful APIs, but I can't say that I've used them.
Twitter offers RESTful APIs. As per Twitter documentation the Twitter API conforms vaguely to the design principles of Representational State Transfer (REST).
I suggest that one should read, at least, the following blog posts by Roy T. Fielding before concluding about REST APIs
After Maglob's pointer to the AtomPub and some further research, I find Google Data APIs to be quite an inspiring source of information about how to structure RESTful web APIs in a proper way (with exploiting all the benefits of the technologies that underlie it).
Sun Cloud API. One of the few hypertext-driven (and therefore RESTful) APIs I know of.
I second Bill's recommendation of Netflix. The Blinksale API is pretty good, too. It places a little too much emphasis on the URI structure and the many "entry points"; it could be improved with a document that has some URI templates to reduce the dependency of clients on URI structure.
The the photo sharing site, Flickr has a great RESTful API and is the one I learned from. It seems to do good job of exploiting the nature of REST in the real world.
From the site:
Photo Upload API