Perhaps the most popular of all discussion boards - not least of which because it's FREE!

phpBB is a highly versatile product with a huge range of features. It has suffered on and off over the years ...

Another great Joomla template site. Instead o paying a yearly subscription though you can just buy individual  (or 3 for 2!) templates for your website. They're very good value for money too.

PostNuke is widely viewed as the grand-daddy of content management systems (CMS's). If you want a site which does everything, with thousands of plug-ins available, then PostNuke is for you.