the majority of my workday is in front of or within an arms reach of a workstation connected to the series of tubes.
My use of the internet for work purposes depends on the type and scope of the project i'm working on. Equipment manufacturers have all of their catalogs, and sometimes their sizing programs, on the internet these days. (on a side note, the websites with the easiest interfaces are the manufacturers with the largest market share, at least in my discipline. basically, if it takes me more than 30 seconds to find at least the category or series of equipment I'm looking for, I move to a different manufacturer.) To finish answering the question, at least once per project I spend as little as an hour, and up to several days looking for and selecting equipment off of the internet.
on my workstation, no programs are constantly running that refreshes data from the internet. our outlook connects to an exchange server in the office, which connects to the master exchange server in seattle, which then runs our email. if our bldg internet connection goes down, or the Alaska-U.S. connection goes down, we lose our email. gmail, gchat, etc, is not run on my workstation, but on my phone.
so far as i know we don't have a workplace policy restricting the use of the internet for personal use. (there are *odd* stories along these similar lines that I won't write down but would be happy to share over brewskis.) even so, we do have a blocker software thing that prohibits youtube, facebook and failspace. so far as i can tell, and so far as i have heard, that's all it blocks. in further reference to the things i won't write down here, i don't see why someone would get in trouble for personal use of intertubes at work.