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There are two things you need to do here:
(1) When creating your forums you need to set the access level to anonymous posting.
(2) You need to edit the anonymous group from under the system admin section so that the group has module access rights, and rights to the recent topics block from under the block access rights if you intent to use it.
However, I would not recommend allowing anonymous users to post on your forums as you'll get hit with all kinds of nasty spam bots, and you also won't be able to identify your users as all posts will be posted from anonymous.
If you are simply wanting to save your users the hassle of having to enter their username and password each time they access your site, I'd suggest you use the auto login hack way before opening up your forums to anonymous users.