Yes. http://meta.stackoverflow.com/questions/2267/stack-overflow-...

To be clear: there is no version of the actual Stack Overflow code that is publicly available. There are, however, numerous open-source reimplementations of portions of the site code.

Also (as the video perhaps mentioned), the Stack Overflow developers have often been able to spin off pieces of the code as open-source libraries. See http://blog.stackoverflow.com/2012/02/stack-exchange-open-so...