Here is the trend I see:
1996 - Classic ASP
2002 - ASP.NET
2009 - ASP.NET MVC
2012 - ASP.NET Web Api and Single-page applications
Perhaps by "RESTful application" you mean a single-page application:
http://en.wikipedia.org/wiki/Single-page_application
This is where the trend is going I believe - instead of creating both UI and business logic on the server side, you can build rich client-side UIs which communicate with the server via REST protocol (thus having only business logic and RESTful endpoint on the server side), allowing you to provide a better use experience to your users. Also you can build multiple UIs for different platforms (Web UI, iOS, Android, Windows Phone, Windows 8 app etc.) which all are consuming the same REST API service.