My viewpoint depends entirely on what job it is you're doing. As a web developer, it would be incredibly difficult to do my job without the Internet. On the other hand, my partner is a technician in school and constantly battles with teachers trying to browse facebook during lessons when they should be teaching. Clearly the latter can have a direct impact on the quality of the job that person is doing. (That's not to say the Internet hasn't affected the quality of my work at times, but I'm not responsible for educating the next generation.)
I'm a big advocate in giving workers a little bit of freedom. I think they're more likely to feel respected, morale is going to be higher and any decent employee is going to give you better results in the long run.
Of course, being responsible for most of the IT has it's advantages - it would be impossible for my boss to install censoring software without me knowing. What I know about, I can circumvent. ;)