I like phpBB3, because the the authentication module makes it (somewhat) easy to replace the internal authentication module with an external one. It makes it very easy, for instance, to allow all gm4il users to authenticate their gm4il id, and use that for the forum. It also makes it easy to integrate with 3rd party payment processors, to manage a for pay forum.
That being said, vBulletin is by far the best solution, out of the box, for running truly large forums, IMHO.
SMF is nice, but I think that there are licensing problems with it that make it hard for third party developers to integrate SMF with other platforms, and while many sites merely need a standalone forum, many other sites want to use the forum as one part of a larger site.