What exactly is RESTful programming?
I think the point of restful is the separation of the statefulness into a higher layer while making use of the internet (protocol) as a stateless transport layer. Most other approaches mix things up.
It's been the best practical approach to handle the fundamental changes of programming in internet era. Regarding the fundamental changes, Erik Meijer has a discussion on show here: http://www.infoq.com/interviews/erik-meijer-programming-language-design-effects-purity#view_93197 . He summarizes it as the five effects, and presents a solution by designing the solution into a programming language. The solution, could also be achieved in the platform or system level, regardless of the language. The restful could be seen as one of the solutions that has been very successful in the current practice.
With restful style, you get and manipulate the state of the application across an unreliable internet. If it fails the current operation to get the correct and current state, it needs the zero-validation principal to help the application to continue. If it fails to manipulate the state, it usually uses multiple stages of confirmation to keep things correct. In this sense, rest is not itself a whole solution, it needs the functions in other part of the web application stack to support its working.
Given this view point, the rest style is not really tied to internet or web application. It's a fundamental solution to many of the programming situations. It is not simple either, it just makes the interface really simple, and copes with other technologies amazingly well.
Just my 2c.
Edit: Two more important aspects:
Statelessness is misleading. It is about the restful API, not the application or system. The system needs to be stateful. Restful design is about designing a stateful system based on a stateless API. Some quotes from another QA:
Idempotence: An often-overlooked part of REST is the idempotency of most verbs. That leads to robust systems and less interdependency of exact interpretations of the semantics.