This is a weird one.
I have Visual Studio 2013 installed. If I create a new project, Visual Studio immediately complains that it cannot find any of the references:
The project does however compile and run correctly, even though there are warnings in the error list:
If I look at the properties of any of these references, their paths are empty. If I load an existing project, Visual Studio can find its references and doesn't complain, even though it is targeting the same version of the .Net framework as the broken project (I've even had them both in the same solution with the same behaviour).
How can I fix this, and what could have caused it? Any suggestions welcome, as it is baffling me.
With thanks to icemanind, I have the answer.
I closed Visual Studio, deleted the following directories and everything is now working as normal again: