"An Internet forum is a web application which provides for discussion, often in conjunction with online communities. Older forums date back to around 1996, following the newsgroups and bulletin board systems which were widespread in the 1980s and 1990s. Popular discussion topics include technology, computer games, and politics, but forums are available for any number of different topics." -- Wikipedia
Message Boards or Forums are extremely popular, and can vary from simple to extremely sophisticated; many formats include member profiles, image/file embedding, visitor tracking and a variety of other features, and can be set up with many configurable options. These are often used as part of full Content Management Systems, though they can stand on their own as well. Examples of popular stand-alone message board systems include phpBB, miniBB, vBulletin and Invision Board.
A few screenshots of a typical message board are below: