vBulletin is a bulletin board system for larger websites.

Both licenses include 12 months e-mail support and access to the latest versions. Both expire after 12 months and a leased license must be renewed in order to continue to run the software. An owned license renewal, for upgrades and e-mail support for 12 months costs $30. 

Both of the above have the vBulletin brand, but branding free is an
additional $120. Installation is $135. Phone support $60 for 1 month, 6 months $180 & 12 months $300.00.

There are lots of hacks available via non affiliated sites and varous independent forums.

http://www.vbulletin.org/ provides official modifications. 

Many sites start with PHPBB (open source) and then move to vBulletin. If you are expecting a large user base you may want to invest in  vBulletin to avoid any user transition and changeover issues.

An open source forum/bulletin board solition.

phpBBS has a very lively developer community and user base. The forum is used on many websites and there are lots of modifications and styles available.

I recommend this for intermediate and advanced users who are comfortable editing PHP programs. It is a good way to start a forum without spending any money.