The internet at work is NOT mine to use as a I wish. It's there as a tool. However, it all depends upon what you do and what your company does.
If I want to play games - then I don't do that on company time. If I've got time to play games - I'm obviously not a trusted employee or else I would be busy!!! :) However, I admit - I'd make time for MAMAPEDIA!!! (DOH!)
I know when I was a receptionist a LONG time ago - we were allowed to play games like solitaire as long as the phone got answered...I didn't like that and asked to edit and type while I was up there...But that's ME!!
There are many today who think nothing of using the internet wherever they are...it's their "right" and they get pissed when the company tells them their services are no longer required....because they were not using the company tools properly....I had one job, as a recruiter, where they monitored ALL of my computer time/stuff...thank God I didn't mess around! :)