As of 2010 this is the best open source forum software. Very Trusted. For Maximum forum security I recommend you install these 3 MODs: httpBL, Stop Spammer and Re-Captcha - they have proved effective in removing 99.999% of robot traffic. In fact, not one single spam post has landed since I installed them - across 4 forums!
The official website for the Simple Machines Forum script. Possibly one of the best forum scripts, it is free and easily customizable. The community is very helpful and there is quite a lot of packages (mods and themes already created for easy installation).