These have all been promising suggestions, but none of them have eliminated the problem. I've deleted .SUO and .SLN files (ankhd, I've not tracked down an .NCB file, though I don't know which "app" you are suggesting).
I did a repair installation of VS2012 -- which I've taken to calling the Mayan Doomsday IDE -- and then just created a new console application. Worked fine -- proper Intellisense, proper Solution Explorer hierarchy of files. Made a "Hello World" that compiled and ran perfectly.
Loaded my Unity project, same damn problem as before.
Loaded an old project, a little thing that I was using to test AI scripts, everything in VS2012 is acting Intellisensibly.
As soon as I sort out my morning errands I'm going to create another new Unity project and see what this one does. I can't say I enjoy the bi-monthly bouts of upgrade issues, random cock-ups, and general incompatibility with modern .NET that Unity Technologies has been providing. Always, always, always blame the tools!
Edited to Add: After completely starting a new Unity project (and deleting the previous one and salting the earth where it trod), everything is working fine again.
Back to my original question, though: What gives? Was this Unity or VS2012? Or me? I tried so many things that I don't know if something helped and what it was.
Edited by GoCatGo, 30 July 2014 - 08:22 AM.