Everyone has a choice as far as discussion boards are concerned, but I'm not enamored with PhpBBB. I prefer SMF (Simple Message Forums), which offer more features, and (at least according to some) superior security. Sure with the latter you'll have to install yourself, but they have a Webinstall.php application/file that makes it real simple, not much harder than the one-click.
Here's our implementation of an SMF board: http://techbroadcasting.com/smf/
If you are interested in a more robust forum, with commercial support, there's also vBulletin, which is used by both hobbyists and commercial enterprises. It costs $160 for a user license, or $85 per year for a lease.
Our implementation of the latter is on a more highly-trafficked site at:
These sites are all hosted at DreamHost, so you can check performance, content, the look and feel, etc.