Seems quite a controversial topic, especially when it comes to bloggers. There are two sides to the argument that goes with anonymity. One is the right for a person to decide to keep their identity out of the public domain while the downside is the ability for some people to use the same lack of identity to act like a moron.
Looking around at some blogs there have been some downright nasty comments left for the author or other commenter's and most of them have no link back to their own blogs. The anonymity afforded to the abuser induces a great sense of bravery to the person who decides to give a miss to debating like adults and goes for the option of name calling and personal attacks. It is very doubtful that in the real world they would act in such a manner, mainly because they would be nursing a fat lip or worse seconds after opening their mouths.
Some bloggers who hold less conventional views and seem to attract the potty mouthed idiots, switch on comment moderation so they can weed out these idiots which is fine but can be used by the more unscrupulous authors to skew the comments they allow on their blog towards there own way of thinking.
Unfortunately, it is the price bloggers have to pay for having a unregulated Internet where we can say whatever we want on any subject we want but i would rather have to put up with the odd socially backward commenter unable to engage in debate rather than make everyone identifiable with their real life details which could lead to all sorts of problems.