We use PHPBB and we're quite satisfied with it . It's incredibly customizable and easy to use.
With PHPBB there's no need to ever switch to a paid forum unless you have forums which have a tremendous amount of visitors per day/posts per hour.
By the way, I expected something else here . I was kinda hoping for advice on who to mask, how to setup your admin rights and how to prevent the wrong people from gaining access, what are good masking systems/forum setups etc .