Where can I get a free template like the Stack Overflow site?

The Stack Overflow template is original to my knowledge and well thought out.
There are many clones and searching will reveal a whole list for you.
If you need something just for your own product etc, then you could easily use this Q&A system
http://www.osqa.net/ which is used on quite a few other sites such as http://ask.sqlservercentral.com/

Justin King (via What template is stackoverflow.com based off?)

There's also this other relevant answer:
Can you create a new Q&A site following the Stack Exchange template?

There's also the option of sailing the seven seas... but seriously, try to d

The Stack Overflow template is original to my knowledge and well thought out.
There are many clones and searching will reveal a whole list for you.
If you need something just for your own product etc, then you could easily use this Q&A system
http://www.osqa.net/ which is used on quite a few other sites such as http://ask.sqlservercentral.com/

Justin King (via What template is stackoverflow.com based off?)

There's also this other relevant answer:
Can you create a new Q&A site following the Stack Exchange template?

There's also the option of sailing the seven seas... but seriously, try to do as much as you can do yourself.

I don't know of a FREE Theme that can do this, but for $29 you can get a single site license of Answers (Affiliate Link) Theme by Templatic. Templatic's Themes are pretty powerful, but can also be a little daunting for beginners.

I personally haven't used this Theme, but do have a Templatic Membership and their support is pretty good as are the support forums.

WordPress or Wix has free templates which you can avail from there. You can download them in a .Zip format.

However stackoverflow isn't based on a template. It's a responsive website developed from scratch without any template. They are basically referred to as dynamic sites.

You dont need a template. Just create a Wordpress site and follow my tutorial:
[Tutorial] Custom front page post loop like Stackoverflow in Wordpress

You will get a very similar behavior. That is just a frontpage of course, but you can customize further :)