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.
On the other hand, people with no lives will thrive on forums requiring registration. Children and Internet addicts tend to have free time to go register an account and check their e-mail for the confirmation message.
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. Quoting a 4channeler:
Trolls are not out to protect their own reputation. They seek to destroy other peoples' "reputation" ... Fora with only registered accounts are like a garden full of flowers of vanity a troll would just love to pick.
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. As Hiroyuki, the administrator of 2ch, writes:
If there is a user ID attached to a user, a discussion tends to become a criticizing game. On the other hand, under the anonymous system, even though your opinion/information is criticized, you don't know with whom to be upset. Also with a user ID, those who participate in the site for a long time tend to have authority, and it becomes difficult for a user to disagree with them. Under a perfectly anonymous system, you can say, "it's boring," if it is actually boring. All information is treated equally; only an accurate argument will work.
Practice making posts in the Sandbox.