Ive seen people praising MyBB a lot more lately.. Maybe thats a sign that its good?
I have experience with phpbb2 and 3 and SMF. Out of those two I'd pick phpbb3.
I used MyBB up until recently, when I bought IPB. I have to say, it was good enough for my uses at the time. I'd use it above phpBB3 and SMF anyway. The only thing though with free forum softwares in general, they haven't quite moved with the times. To get a half decent profile for MyBB, you need to get this plugin. Even with that, it hardly compares to this layout in IPB.
Personally, I feel that MyBB will give you all the basics you need to run a forum. However, if you want anything more, you'll have to go and search around for plugins. Most plugins can only be got from paid sites like MyBB Central and MyBB Source.
I have owned a forum phpBB, MyBB, SMF, IPB, and vBulletin.
When it comes to just the free stuff, MyBB would definitely get my vote in its ease of use and a simple templating system which only requires (x)HTML and CSS.
SMF is really easy to use as well but the uncertainty of the project and also Project Phoenix will send it to its demise. However, ease of use and its efforts to strive for validations of standards give it honourable mentions. SMF's package manager feature also does it all. Uploads AND installs mods, upgrades forum software, you name it.
phpBB has always been the furthest behind. It took them years to finally get Quick Reply and some RSS features. The file edits system makes things a pain to upgrade and overall, there are better options.
Mind you, although SMF is freeware, it's not technically open source. It's under its own license and not under one of the licenses approved by Open Source Standards (GPL, LGPL, BSD, MIT, Apache to name some). Forking and copyright removal are also prohibited as further examples. I won't get into IPB/vBulletin today, since this is about the free stuff.
I vastly prefer SMF to MyBB, but the recent chaos with Project Phoenix does make the future of SMF look grim. I don't mind MyBB, and I think it's way better than phpBB, but I think you can do so much more with SMF than you could with MyBB. I might use MyBB for a small roleplay forum, but I'd never use it for a larger site. Being open-source and not updated often alone would make my decision, but there are so many more mods for SMF that I can pretty much do anything with SMF that a vBulletin site could do, and for free.
