I did a lot of research on this about seven months ago when I was looking for a good kb for our website. There are loads of free so-called kb systems but most are just adaptations of either a FAQ system or a CMS.
In the end, following a number of recommendations, I purchased PHPKB Knowledge Base Software from knowledgebase-script.com. It's not free, but it comes with full source code and it is easy to set up and use, reliable, secure, and easy to customize. They responded to my purchase enquiries quickly and on the one occasion I need to query something, I got a very quick and informative response.
I particularly like the way someone can ask a question and before it is submitted, relevant possible answers (suggestions) are returned. They offer a 30-day evaluation trial so you can see for yourself whether it is a good fit for what you want a KB software to do. I researched and tried a few scripts, but at the end of the day the cost of buying PHPKB was less than the cost of my time messing around trying to change cms/FAQ/wiki type scripts to do what I wanted.
