I work for local government, not sure what is and isn't monitored. I don't have any desire to look at gaf or reddit or anything as long as I have work to do.My internet definitely gets logged but not actively monitored. Anywhere that your internet gets actively monitored is fucking crazy Big Brother shit (i.e. the government!).
Internet usage would only really come up if you're an idiot and go on a porn site and have it be flagged, or they're looking for a reason to fire you.