Best not to use your work internet for personal stuff, even if it's just reading the news. Most companies scrutinizes the logs at times, and they do keep them in record and will use them against you. I know two people that I worked with who got fired for downloading child porn at work!
Get a decent internet connection at home where you can do what you want, and use the work internet only when absolutely necessary--always check the links that you follow. Don't blog under your own name, don't send personal mails from your work email, and most importantly--don't do any personal stuff, or EVER play games on your company's computer.
Paranoid? Maybe... I'm talking from years of experience working in the banking, mining and government sectors. Management DO check up what you do on your work PC.
If you are serious about your professional career, you really do not want anything that can be held against you if things do not go your way for some reason.