Depends on the site. If it's just a forum, then I'd use myBB If it needs to be integrated into a CMS then it depends on the CMS. I'm familiar enough with Geeklog and Wordpress to suggest using phpbb with the geeklog integration plugin and RS Discuss for WordPress. (RS Discuss is really barebones but for most WP sites it works well) If it's some other CMS then I don't know.
http://www.phpbbhacks.com/ has so many PHPBB hacks that you can make your site into a vbulletin site. So far, I added a hack that shows the latest post on the index page, and a hack that will put a quick reply. You can check it out at www.videoforumclub.com
This site allows you run side-by-side comparisons of nearly every forum package out there: http://www.forummatrix.org/
am using phpBB, this is the best and it's widely used in the net so the visitors are familiar with it