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NO REGISTRATION NEEDED
Registration keeps out good posters. Imagine someone with an involving job related to your forum comes across it. This person is an expert in her field, and therefore would be a great source of knowledge for your forum; but if a registration, complete with e-mail and password, is necessary before posting, she might just give up on posting and do something more important. People with lives will tend to ignore forums with a registration process.
Registration lets in bad posters. On the other hand, people with no lives will thrive on your forum. Children and Internet addicts tend to have free time to go register an account and check their e-mail for the confirmation message. They will generally make your forum a waste of bandwidth.
Registration attracts trolls. If someone is interested in destroying a forum, a registration process only adds to the excitement of a challenge. One might argue that a lack of registration will just let "anyone" post, but in reality anyone can post on old-type forum software; registration is merely a useless hassle.
Anonymity counters vanity. On a forum where registration is required, or even where people give themselves names, a clique is developed of the elite users, and posts deal as much with who you are as what you are posting. On an anonymous forum, if you can't tell who posts what, logic will overrule vanity.