If you use Fiddler (on Windows), it will set your proxy settings to http=127.0.0.1:8888;https=127.0.0.1:8888.
If, for some reason, it doesn’t shut down cleanly, it won’t undo that proxy setting, and your internet will cease to function.
At first I just rebooted, but I still had no web access. I could ping 188.8.131.52 so I knew I had connectivity. I could ping www.twitter.com, so obviously DNS was resolving. The proxy setting was the next thing I checked, and there it was, mocking me:
Turned it off, and voilà!