Main Advantage to using ASP.Net MVC vs web forms

ASP.NET Web Forms:

• Development supports the state • Gives the illusion that a web application is aware of what the user has been doing, similar to Windows applications. I.e. Makes 'wizard' functionality a little bit easier to implement. Web forms do a great job of hiding a lot of that complexity from the developer.
• Rapid Application Development (RAD) • The ability to just 'jump in' and start delivering web forms. This is disputed by some of the MVC community but pushed by Microsoft. In the end, it comes down to the level of expertise of the developer and what they are comfortable with. The web forms model probably has less of a learning curve to less experienced developers.
• Larger control toolbox • ASP.NET Web Forms offers a much greater and more robust toolbox (web controls) whereas MVC offers a more primitive control set relying more on rich client-side controls via jQuery (Javascript).
• Mature • It's been around since 2002 and there is an abundance of information with regards to questions, problems, etc. Offers more third-party control - need to consider your existing toolkits.

ASP.NET MVC:

• Separation of concerns (SoC) • From a technical standpoint, the organization of code within MVC is very clean, organized and granular, making it easier (hopefully) for a web application to scale in terms of functionality. Promotes great design from a development standpoint.
• Easier integration with client-side tools (rich user interface tools) • More than ever, web applications are increasingly becoming as rich as the applications you see on your desktops. With MVC, it gives you the ability to integrate with such toolkits (such as jQuery) with greater ease and more seamless than in WebForms.
• Search Engine Optimization (SEO) Friendly / Stateless • URL's are more friendly to search engines (i.e. mywebapplication.com/users/ 1 - retrieve user with an ID of 1 vs my web application/users/getuser.aspx (id passed in session)). Similarly, since MVC is stateless, this removes the headache of users who spawn multiple web browsers from the same window (session collisions). Along those same lines, MVC adheres to the stateless web protocol rather than 'battling' against it.
• Works well with developers who need a high degree of control • Many controls in ASP.NET web forms automatically generate much of the raw HTML you see when a page is rendered. This can cause headaches for developers. With MVC, it lends itself better towards having complete control with what is rendered and there are no surprises. Even more important, is that the HTML forms typically are much smaller than the Web forms which can equate to a performance boost - something to seriously consider.
• Test-Driven Development (TDD) • With MVC, you can more easily create tests for the web side of things. An additional layer of testing will provide yet another layer of defense against unexpected behavior.