While debugging VS2012 I have found that I can no longer access variable values:
I've eventually managed to sort this out by myself - so I'll give my solution here in case anyone else has the same problem:
I found that in Tools->Options->Debugging->Symbols was pointing to an old NuGet symbol server. Somehow a wrong symbol server looked like it was taking down the entire Locals and Immediate Window systems.
Updating the symbol server fixed my problems.