I think the future of REST is bright. The benefits of REST are substantial, and as a result RESTful services are becoming more and more common. In some form or fashion, I see REST being around for a long time.
Hmm. I just realized that I'm not really all that sure about what is the reason RESTful applications or interfaces are important? What is the added value that I as a CEO get out of it? What's the business case?
For me, the business case for RESTful design (in Rails, specifically) has a couple of parts. First, it makes development faster and better by imposing more constraints on the process (much like Rails itself does) and making systems more predictable. As a side effect of this, maintenance and extension are easier down the road, as well.
Second, using REST means that your web service layer sits closer to your web application layer. This means that it's easier to build, manage, and update your service offerings while keeping them in sync with your public site.