Othellotech is correct, there are so many different factors. It's almost impossible to say. Back just a few years ago, it was common to run a server with 4gigs of ram and a mid line CPU and host a bunch of phpBB forums who just wanted to talk about games, guns, you name it. Now with WP blogs, graphic intensive CMS programs all tied in, you can really suck up the power and load up a DB really quick.
However, I tell people unless you really know your audience, or are moving an existing forum that runs a lot of traffic, start small even if only on a shared hosting platform, till you build your traffic and subscriber base up. Then get something better because it is no big deal to upgrade or move into a larger / dedicated server.
Plus it's better on the wallet also.