After installing Visual Studio 2012 and opening my solution I get a series of errors in this form:
The Web Application Project Foo is configured to use IIS.
Unable to access the IIS metabase. You do not have sufficient privilege to access IIS web sites on your machine.
Thank you to everyone that answered. Since this was closed for a long time I couldn't provide much feedback, but I did eventually fix my problem. I tried many of these other solutions and they didn't fix my issue, but I'm sure they help when the root cause is different.
I solved this problem by turning off the IIS and .Net Framework features within Windows 7 and then turning them back on. It seems like this re-installation is what fixed my issue. I still don't know what caused the problem, but at least one other developer on my team had the same issue.