Question & answer websites (like Stack Overflow) are great platforms for enabling communities to share knowledge and help each other.

Although they are kinda similar-in-function with the forum applications (check 9 Widely-Used And Free Forum Softwares), the main focus is finding the (best) answers.

Here are 5 free and open source or hosted platforms to create your own question-answer website:

Question2Answer

Question2Answer is an application that is built with PHP-MySQL that has a points-based reputation system.

Users can comment into any questions and they can be tagged.

It can be totally styled with CSS and has an admin interface to manage the whole application.

QSQA

QSQA enables anyone to instantly create a full-featured question-answer community where users can earn point/badges for their contribution.

It is written in Python and powered by the Django application framework.

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Jutda Helpdesk is an easy-to-use & open source trouble ticket system that is built with Django.

Whether the tickets are sent via the web interface or e-mail, the application can create the ticket & users can reply to e-mails to continue the conversation (e-mail piping).

It can be enabled to accept tickets from non-registered users which also makes it possible to be used as an advanced contact form.

Tickets can be separated into departments, product-groups, or any other classifications. Also, they can be escalated automatically between users by priority.

The application supports multiple RSS feeds & has an API for integration with 3rd party products.

P.S. Jutda Helpdesk is currently in alpha status yet very promising.