I used to work in an office and people played online all of the time. Some, WAY too much. I don't see a problem with it here or there, as long as your work is complete. Of course, now that I'm the owner of a business, I might get online, if I'm bored but I don't let my employees. I'm paying them to work.
I worked while I was at work but I worked with people who spent the whole day online shopping and playing. Call me old fashioned but I think you should be doing the work you're being paid to do while on the job.
I had to go to the property assessors office today. When the receptionist/worker went to make me copies I took a peak at his computer monitor (work computer) and in a smaller screen in front of some obvious work material was an internet card game. So I'd have to say he be on this side of the rivalry.