phpbb2 has quite a history of security vulnerabilities due to the fact that it was poorly coded, phpbb3 looks a bit better (code wise) still it's not as trustworthy as vBulletin and IPB. Recently SMF had a sudden outbreak of security vulnerabilities, so my advice is to go with a paid commercial product if you're serious about your forum.
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A few years back my favorite was Invision, but that is no longer free and I have not used it since the free version was around.
I'd have to say the "standard" for open-source forums is PHPBB and it does a pretty good job. However, vBulletin seems to be the best when it comes to large scale communities, although its not a freebie.
Personally i love #4, Vanilla. It's hard to modify but it has an amazing communit and lots of great addons
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