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Another resource-oriented pattern for implementing task services and handling the equivalent of statefulness has been used successfully in real-world applications by Rob Heittman, and may actually be a concrete example of the first bullet point, above:
The classic example of something very hard to implement without some server side state is an e-commerce shopping cart. There are a handful of examples on the web of a "purely RESTful shopping cart," but they tend to be a bit odd ...
But one way to RESTify this model, without changing it completely, is to deconstruct the idea of the "session" a bit. Instead of having one generalized server-side bag of state (the JSP/Servlet style HttpSession), which can only be accessed using server-side code, the client can use RESTful operations to create a needed resource on the server (e.g. a ShoppingCartResource); then these resources may be exposed back to the creator using RESTful patterns.
This hypothetical ShoppingCartResource would have a URI and ... representations that can be PUT, GET, etc. ... Now you have your shopping cart abstracted in a way that you can work with it on the server side using internal requests ... OR work with it on the client side using an Applet, Flex/Flash RIA, GWT, or AJAX application.
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