These questions have been asked a few times before so rather than regurgitating what has already been said here are some links that should give you all the information that you are after:
Biggest advantage to using ASP.Net MVC vs web forms
Comparing Web Forms And ASP.NET MVC - MSDN Magazine
http://blog.mikecouturier.com/2011/03/aspnet-web-forms-versus-net-mvc.html
But my thoughts very briefly are:
The MVC framework (asp.net) has been out since 13 March 2009 when the first stable release was.. well released.
Between then and now the team at microsoft have made a huge number of improvments and I'm sure into the future they will make even more.
They key point for me is testability of applications built in MVC. They are just easier to Unit test, this might not be important to you.. although it should be.
Dependency injection is another thing that is "baked in" with MVC 3, if you like the SOLID principles then DI will be something you are interested in.
Then there is the flexibility of it, This article talks about the 13 points of extension, It is a little out of date now, but still worth a read.
For me it's all about the benefits of MVC over webforms.
With all that said I have to ask you
Why would you not use it?
And I am aware that you might have a good reason not to, one example might be if you have a team of developers who are all control gymnasts with a love for viewstate and things webforms then a move to MVC might not be a good idea for you.