My favorite software for creating forums is Simple Machines Forum, or SMF for short. It’s a free PHP forum script that I believe surpasses phpBB in quality and feature set (though I haven’t tried the latest phpBB version yet).
One problem, however, is spam. Virtually all forums are plagued by spam posts and user registrations, creating hours of tedious work for the administrators.
If only I’d found it a year ago, when I really needed it!
I will take this opportunity to point you in the direction of the Akismet Development page. If you head over there, you can find libraries for PHP and other languages, as well as plugins for other CMS and forum scripts (like phpBB or Joomla). Akismet can be used nearly anywhere that comment spam is a problem.