I use
www.freeforums.org and I've been using them for years, love their service. They have phpBB3 forums completely free of charge(phpBB3 is like, the next best thing if you don't want to go with vBulletin), basically you just build it from pre-made forum(You add in your own titles and sections and all that), add your own custom template or choose from hundreds of their pre-made templates, then you're done. You can check out mine as an example if you want, it's at
www.forums.horror-junkies.com What I did, which you could also try, is I set up this forum for free back when I was working majorly on my project, but had no funds for a domain. Once I got the money, I registered the domain, then I just set the forum up with the custom domain name.
Proboards is also a slightly decent choice. Not as good as freeforums.org but if you're really savvy with customizing forums or using hex codes for colors, it's a great place to use. It's extremely customizable if you search for pre-made skins from other people and apply it(Like a Myspace layout). I have a few examples you can check out, at
www.amandayoung.proboards.com www.hillshaveeyes.proboards.com and
www.horrorjunkies.proboards.com
A lot of people that want a vBulletin, but can't afford it or don't want to pay for it usually go with Invision Power Boards, they have a somewhat similar design. You can check out a pretty bad-ass example here-
http://z14.invisionfree.com/Supernatural/index.php? I'm not too familiar with their features and options, as I only used them one time about 6 or 7 years ago, but they are a pretty good company. They've been in the forum game for years, and obviously, the customization as far as layouts goes is pretty good.
It really just depends on how much you want to be in control of customizing your own forum, what designs you are looking for, and a few other things. Personally, I highly suggest
www.freeforums.org they're a great place and have a large amount of features and templates to customize your forum.
I've been setting up forums for people and myself for years, so if you are interested in any help, let me know. I'd be more than happy to help you find a place that suits you and help set up/customize the forum if needed.