I am a complete and total convert to ASP.NET MVC and have not looked back, that said I do still have to maintain several very large WebForms apps. Here's my take on it:
Use these when you have some serious heavy lifting to do with grids. The grid controls are really very nice when you have a simple dataset that fits nicely in a tabular format and you want to provide a simple way for users to update records. Yes, I know that MVC 4 has a really snazzy Ajax list-type thing that you can use which works great but, in our business we often need to get something running yesterday and good old-fashioned grids work great and users are happy to be able to tab across a grid with glee. For me that's really the best thing about WebForms for me; but, as Ryan pointed out WebForms can be a big time mess because you're playing both sides of the fence from a nifty code-behind file. It can be both a rose and a thorn at the same time to keep all of your controller-type stuff intermixed with your view(s).
Use this when you really want to roll your own and you have the opportunity to start an application from scratch. Having a clearly defined MVC application is a bit more work to get started with but its benefits in maintainability outweigh the initial setup cost. If you want to do interesting Ajax interactions, prefer to write your model with code, like clean url's and routes, and be able to control the entire flow of your app then this is definitely the way to go. It takes some getting used to at first but I think it's the better option for greenfield apps.
In conclusion, for me, it comes down to grids and !grids. :)