From the "outsmarting yourself department": Yesterday, I installed Team Explorer on my machine to get access to a CodePlex project. Easy enough, at least that's what I thought. So after installation I went to Visual Studio to configure the server connection, but I ended up not being able to connect:

As I was in a hurry anyways, I decided to leave it at that. Fast forward a few hours, to a different location: a pub. I was discussing IT problems with a friend, and at some point we got to firewalls. That's when I went "Bingo!" - this Vista machine has Privoxy installed, to "emulate" Firefox's Adblock extension (Privoxy does a few things more - check their Web site, it's free). And IE7 is configured to use it as proxy server.
So first thing today was to get back into Visual Studio, try again, and then check the Privoxy logs:

Note to self: The TFS client APIs use Internet Explorer settings when it comes to connecting to the Internet, and Privoxy positively strips requests of certain headers.
Fixing is easy: Tools / Options / Environment / Web Browser:

And then add exceptions for all the TFS servers you need to access:

Security does tend to get in the way. Nothing new here.