I would personally go with a free host rather than a free forum host because they will allow you access to the database and files if you ever want to purchase hosting and move your site.
Personally, I think that Jcink Forum Hosting (Jcink.com) is the best.
JFH allows you to take copies of your database whenever you want for free.
JFH has built in (but optionally whether they are enabled) store, arcade, gallery, shoutbox, and more mods. (Plus a bunch more options as seen here that set it apart from other free forum hosts.)
JFH has been around for over 6 years now so they have a fairly long history of providing quality service to users.
If nothing else JFH is definitely worth having a look into.
I know a free host would be better, but i want it to be on a free forum host. 😛<br /><br />-- 08 Jan 2013, 05:50 --<br /><br />I want a free forum host, becuase i want that 'hosted on a free forum host' look. 😛
We are in the process of creating a new theme for the site and forum, so do not let that turn you away. we are not packed with modifications and style like other hosts are as we focus on the speed and quality of your forum first. If your forum is down every hour, what good is it? We are, however, testing and installing modifications over the next few months. We are always taking suggestions for new modifications, styles and features to add to our service, so if you don't see something that I you really want, feel free to request it. We do charge for backups, but the fee is very small, compared to other free forum hosts.
If you have any questions about our service, please do let me know via PM as I do not want to fill up your topic with questions and answers. 🙂