After learning Backbone.js and using it on a few projects, I've found that most of my time is spent figuring out how to use it, and not what my backend is doing. In terms of ASPMVC, you setup a few controller actions that return JSON.
Rob Connery uses Backbone.js with MVC3 in his series Real-World ASP.NET MVC3 on Tekpub.
Episode 6 - BackboneJS - is spent entirely introducing you to backbone and ASPMVC3 integration. Unfortunately, you must purchase the entire series for $32 and it helps to watch the whole thing to get a sense for whats being built. Further, I don't agree with the way he approaches everything in the videos but his use and description of Backbone.js is very helpful if you are new.
DocumentCloud (the project from which Backbone.js emerged) maintains a page entitled Tutorials, blog posts and example sites. They don't always list the backends used so you may have to browse all the links to see if you find anything.
This is quick little tutorial from real-world experience, basically wiring a backbone application to some ASPMVC endpoints.
Finally, here is a recent post on Microsoft's own ASP.NET Weblogs called "Integrating Backbone.js with ASP.NET Web API".