A next-generation forum script with better security then it's predecessor, phpBB2. It's a free script that has been downloaded millions of times and used on an estimated 6 million websites. A webmaster could easily find modifications (MODs) to add features and even free web templates for your forum (styles). The project is run by the phpBB Group and they always release under the GPL license.
An example site that uses phpBB3 is www.phpBB.com