I think that PHPBB is the best. I also used it in my forum with good look and a lot of option for customizing the temples and customizing the forum. You can see the sample at Best IT Forum
It seems like 5 years later vBulletin somewhat won the war, but with their release of version 4, I was not as impressed. I like 3.8 a lot better, but hopefully 4 will start to work out the kinks. Seems that phpBB is still alive but not nearly as big as in the past. I don't here about Simple Machines too much, but I assume some still use it.
I prefer phpbb3.. especially the SEO'd version.. http://www.phpbb-seo.com/en/phpbb-seo-premod/seo-url-premod-t1549.html
I´m a total newbie here and in the whole forum administration field but: I recently started my first forum from scratch and used PhpBB free forum software. Knowing practically zero about all this it was a bit of an ordeal but I managed to pull it off thanks to other how-to forums and the phpbb how-to forum specially. And the result was actually very good. Exactly as what I had envisioned. As a I said, I am a newbie on this so I can´t compare phpbb forum software with others but I can tell you that is a great looking software and it can be set up by someone who doesn´t know anything about programming (like me). Anyway, my 2 cents.
PhpBB3 is best free 4rum. easy to control, easy setup and most sercurities I know and use phpBB from phpBB2 now still family with just installed Insurance forum at bảo hiểm Việt Nam
+1 for MyBB, it's easy to use, has some great free themes that look like premium themes and it's free.
I have one question about Free forums...At a time in the future, Say you want to change your free forum to your own server. How difficult is it to transffer the free forum to your own server from the free forum server? And which free forum software can you do this with?
MyBB is the best free set-up in my opinion. As for best overall, I think Xenforo just sneaks ahead of vB.
Thank you all for sharing these free online resources. Now that I have started my online career, I can study about the online softwares and fully utilize these to work more efficiently with my online jobs.