I\'m trying to understand how I will be able to craft an API using ASP.NET Web API which will be protected from CSRF, while still being accessible from non-web environments (e.g
CSRF only becomes a problem when you are using a persistent auth mechanism such as cookies, basic auth, NTLM etc. Mike Wasson has an example of using CSRF against webapi in Javascript - and I've seen versions in DelegatingHandlers ....
As CSRF is only a problem in web scenarios you can argue there's no real need to check for non-web requests. Every ajax request from a browser, whether via jquery, the native XmlHttpRequest classes or whatever comes with a header - X-Requested-With, which will have a value of XMLHttpRequest. So you could limit your CSRF checks to just requests with that header, as anything without it must have come from outside a browser.
Having said that if you are authenticating, I'd look at some sort of shared secret or OAuth mechanism, and have a DelegatingHandler server side to validate, and in the web app just put the token somewhere that it can be picked up via javascript and sent via an X-Authentication header - as it's not persistent and needs to be attached to every request (just like the CSRF token) there's no CSRF problems. Dominick, as ever, documents this sort of thing well.
Have a look at the SPA templates in the latest MVC4 update. They have a sample implementation for Anti-CSRF for Web API.
Take a look at the CORS implementation for WebAPI.
http://blogs.msdn.com/b/carlosfigueira/archive/2012/07/02/cors-support-in-asp-net-web-api-rc-version.aspx
Then you could allow only localhost as a valid URI on the webapi server. This would prevent other sites from loading attack code in the browser.