It depends on your scale and how much of your server's resources you want to dedicate.
I help manage SFRedbook.com, a Northern California escort board with 20,000 members. It runs on an old hacked version of the PERL based DCForum cleanly and with a powerful dedicated server serving hundreds of thousands of pages a day.
PHPbb is a good product, open source with a huge development community, but slightly slower. VBulletin is good. DCForum+, a PHP version of the classic forum, is good. With any PHP/MySQL product, speed and scalability depends on the install tweaks to the database. The problem with these PHP products are they're easily hacked.
I like Gossamer Threads, PERL based/SQL. It is fast, robust and difficult to break.
http://www.gossamer-threads.com