Surely there are cases in which anonymity is a good thing. I'll leave you to supply those cases for yourself, but there is a pernicious sort of anonymity on the web, the kind that leads to trolls and others who post comments on fora, on blogs, on websites for no more reason than to cause aggravation in others and a delectable Schadenfreude for themselves. This very sort of anonymity infects even social networking sites, so that people who claim to be friends will post—from the distance of the web and the pseudo-privacy it affords—comments that they would never utter if they had to defend themselves or face another person as they did. This, I think, is another way that virtual friendship and communication can coarsen human relations and erode civility. We all have Tourette's now.
In the more personal case, I came to see people that I liked and respected acting (virtually) towards others in a way that took me from enjoying the prospect of seeing or talking to them to hoping I might never have to talk to them again. Comments directed at me never much bothered me; I bartended for five years, I'm gay, I teach college students, so insults and snide remarks I can handle. But seeing people pounce on innocent others and judge from the height of their digital tower, I enjoy not so much. Perhaps I'm oversensitive, but I don't need a website to provide me with that kind of interaction. I can get that much easier.
I remember once being told not to say anything that I wouldn't say within my mother's hearing. An apt corollary for the web might be not to type anything you wouldn't say to the person in person.