Top free open source Question and Answer Engines for Websites
OSQA – The Open Source Q&A System
WordPress with DWQA plugin is a good option for easy integration of wordpress to SEO, you do not need to use paid themes or special QNA themes, it works with your website and you can make a page o integrate qna to your existing wordpress by using shortcodes. Widgets are also available in this plugin for recent, most popular and top questions.
Shapado is also well-known QNA engine, it offers some unique useful features, such as answer by email, community building and marking answer as improve so that others are able to edit your answers.
Database : MongoDB
License : GNU Affero General Public License
Responsive, fast and built in php, it is extremely easy to integrate with other php based web engines.