Does anyone know of a php based forum that is easily customizable to work with an existing user base so that members don't have to register or sign in a second time when they access the forum? I heard that this is possible with phpbb3 but I haven't seen anything in their documentation that covers this.
you heard right, but that is the user's choice. If the user TICKS THE REMEMBER ME CHECK BOX, then it remembers the user provided that the user do not clean his/her cookies or cache for that matter. phbb3 is a powerful one with a lot of features and to know more u might wanna give it a test.