ASP.NET MVC has gained a lot of prominence for Web Applications, since .NET is used a lot in the industry.
Microsoft web applications evolved from Classic ASP to ASP.NET, which is based on Web Forms (to allow the skills VB6 Win Forms developers already had to be easily translated to the new frontier of the web).
Unfortunately, Web Forms is state-based and HTTP (that the web is based on) is stateless, so a lot of nasty workarounds due to things like viewstates were needed.
ASP.NET MVC allows the skills WebForms developers have to be translated to a web framework that has good SoC and that has had a lot of effort put into being testable (since WebForms isn't very testable, the MVC team have put a lot of effort into the framework).
That said, it's not a panacea/silver bullet, and like any framework, there are times to use it and times not to use it. Hopefully people won't use it to try to solve everything, after all: when your only tool is a hammer, every problem looks like a nail.