bbPress is a forum plugin for WordPress and WordPress MU sites. It was made by the developers of WordPress and is easy to integrate with an existing WordPress or WordPress MU blog.
Some people prefer to use other standalone forum scripts such as VBulletin, phpBB, or SMF with WordPress MU and use a "bridge" to tie together the login details from the two databases. This can work well and is certainly a good option if you have a reason for wanting to use a standalone forum. (Perhaps you have already purchased a license for VBulletin, or you have a heavily modified phpBB install with a large user base, and don't want to confuse your users by making a change.)
However, if you are building a brand new site, then the advantages of bbPress are huge.
bbPress has been developed from the ground up to work with WordPress and WordPress MU.
It can easily be modified to share the theme of your WordPress site.
It has "pretty permalinks", just like WordPress.
It is stable and fast.
The ties to WordPress mean that when new versions of bbPress or WordPress are released, any integration issues will be fixed promptly.
There are lots of plugins available to add new features to your forum.
You can find out more about bbPress at http://bbpress.org/.