If you're not really into the technical mumbo-jumbo, www.makephpbb.com
offer a great free hosting service for phpBB forums. They have many MOD's, languages and styles pre-installed, have never gone down in my experience, and are pretty fast.
But if you want to manage your own forum fully, then you're best off with a paid host.
IPB and vBulletin and pretty hard to use and configure, and cost a bomb, but they are very reliably and feature-packed software packages.
phpBB and Simple Machines Forums are both good, free forum software.