Well, I've had some personal experience with a few message board softwares in the past... so let's see....
Invisionboard: The free trial option of invisionboard never expires, so yes, it's still free!

IMHO invisionpowerboard (IPB) is the best free forum software out there. It's similar to phpBB and vbulletin in the user-side interface and concept as many of the default features are similar. But when you look at the adminCP, it just stuns me everytime on how many features and the powerful tools that are unique to invisionboard for the Admin-side. I've grown accustomed to relying on this tools. But if you're computer technology impaired or if you simply just want something simple, I would suggest you turn to vbulletin or phpbb, depending on whether you want to do a paid option. And with the ability to put loads of modifications, skins, and customize it, IPB is just as powerful as any other forum on the modification level, DESPITE some common belief among phpbb users that IPB can not be modified.
Vbulletin is probably the best option if you're going to be paying for your bulletin. To tell you the truth, I'd rank vbulletin just a tad above phpbb due to its unique user-interface that allows for threads to be organized or created in a different scheme than other forums do. In other words, they have a thread branching system that was a new feature in their their newest version that came out recently (2.3.4). Another big pro is that there are MANY premium vbulletin skins out there that look absolutely beautiful. However, other than that I can't say much about this. If you're tight on a budget, I would not recommend this option.
phpBB is a great message board. It's what the servermatrix forums is running off of right now. However, as an IPB user, I think phpbb is a little too limited on the admin side for me. I love how it's GPL licensed, meaning that it'll always be free. Another pro is that a lot of modiifications released are supported/created by the phpbb dev. team. And this is another free board option. If you want the same user-side power as invisionboard and vbulletin, but want a simple admin-side that'll get what you need done, then phpbb may be the option for you.
xmb: xmbforums is IMHO one of the simplier forums out of the ones I know. I know some people choose them because they are slightly technically impaired and need a relatively simple to use forum, but sometimes I think it's just because they havn't discovered invisionboard or phpbb yet

And yes, this is another free forum, though much more limited on both the admin and client side than the other three mentioned above.
yaBB: I have no personal experience with yaBB, but from what I've browsed through and seen, the client side seems just as powerful as phpbb, though it may lack a few aspects. I havn't seen the admin-side recently, but I know that it's simplicity is similar to that of phpbb in terms of the admincp.
Ikonboard: Ikonboard is a beautiful forum. However, the reason why it would be last on my ranking system is because it's a cgi-based message board. And for those of you who aren't aware, cgi-based message boards will hog up your CPU and server resources like a fat pig after a diet when the board is "fairly" active. I personally know this for a fact as I've had to remove cgi-based message boards from the server before. But as Dustin (Escaped) mentioned, ikonboard is relatively the cgi version of invisionboard, though ikonboard has been here longer.
Well, that's all I can remember for now. Cheers.