If you are looking to run your own online forum then there are a lot of free hosting services out there this google search lists all the free hosts out there. My chosen free forum host is freeforums.org. You get a lot for free and there is a paid upgrade that gives you a custom domain, removes all adverts and copyright and gives you a forum backup option. I'm currently on the free option as my forum hasn't really taken off enough to require most of the paid upgrade options yet.
So if you are considering setting up a forum for your blog, community group, sports team or website and want to give it a go without committing to anything paid until you know that it will be worth the money then try freeforums.org as you get your forum for free an can expand it with any of the paid upgrades that you require.