I'm looking content management system that would have features similar to stackoverflow:
Users can ask and answer/questions. Users can search within existing threads. The system is access controlled - so some users can be readers/writers/admins. Some or all QnA threads should be visible only to logged in users.
So far I've mostly used wordpress as CMS but it looks like it's not well-suited for this particular task
Just about any forum software will meet the basic requirements outlined above. The reason Stack Overflow is so successful is because it was specifically designed for this user domain. Wordpress? Yech! Its backend is spaghetti. :)
Its not free and is hosted but you can have your own stackoverflow from the people who created it! More info here: http://meta.stackexchange.com/
WordPress is ok as a CMS, but really just for publishing articles within a framework and simple commenting. If you want something as nice as StackOverflow, you can license it commercially.
PHPBB2 is a good open-source bulletin-board style forum, and VBulletin is a commercial option. They both use PHP, MySQL, etc..