This question might be a little subjective, but I will take a crack at it anyway.
--Background:
MVC was picked for me before I started at my present company and I was charged with learning it, which suited me fine as I am very HTML oriented. The project is in development but we have iterative meetings to show progress and flesh out requirements. In one of these meetings I found a major payoff:
--My Experience:
The question of whether the site could support mobile phone access was put forth but up until now I had been designing the site for a 1024 x 768 minimum resolution. No worries, I simply turned off CSS Styles and the page displayed in a not-very-pretty-but-very-functional flow. The entire site is designed semantically making it easier to port to different front ends via style sheets and maybe a little JS. ASP.net MVC is awesome for semantic websites, which are cheaper and easier to maintain.
--More Stuff
This is one of several benefits of adopting a web technology that more fully embraces the medium it runs on. Others include:
Better separation of model view and control logic, because well its MVC, but this makes you code more loosely coupled, and more single-responsibility-principle adherent ultimately making it cheaper to maintain
More standards based, meaning its easier to use JQuery and CSS tricks that all the cool kids are using, because those really shine in well formed sematics-based documents. This means its cheaper to add flair
Restful, URL - driven requests. Your URL does not specify some .aspx to load and do a ton of work across a bunch of layers in its poor little code-behind. Your URL specifies a request which causes the router to invoke model-layer functionality which runs where it is supposed to, then dumps pertinent data to a view. Lots of good stuff here:
This makes it easier for one controller to serve up pages, webservices, AJAX, and handle all CRUD cases, but all around a single context.
Each responsibility is handled by a method called from the router, each group of related responsibilities can be materialized into a controller.
You control what data goes where, you can custom build a view model to go out to the view, and the view simply contains logic to show it, making things simple and secure especially if the people working oon the view are not the people working on the controller logic.
There's a lot more but in the time I have taken to type this, all the other answers have probably been posted.