I have heard many stories from people who had their sites integrated elsewhere so that the visitors to those other sites would see the original one not even knowing that the sit
Someone might try to make money by showing ads bundled with good content (created by others). Lots of good content = lots of visitors = lots of clicks on the ads = some money. Of course it's wrong, but there's certainly no way to prevent it technically. As long as you can read it, a machine can copy it.
I guess the only solution is to maintain an ever changing website, to which users come to see the new content and interact with it in such a way that comments fuel new content. Then going to a mirrored vesion will be seen as an inconvenience to both users and authors. Of course, this wouldn't prevent mirroring, but only makes it less worthwhile, hopefully.
In short, you can't. But fortunately, they can only copy your front-end data. Your CSS, Markup, and JavaScript are all out there. You should state in your footer that your content is your property, and may not be copied or distributed in any manner without prior consent from you. That won't deter anybody motivated enough to copy in the first place, but it gives you better footing for any future disputes.
Some measures can be taken to really make the process of stealing your content rather tedious. Many users will obfuscate their JavaScript, making it practically unintelligible (without programmatically cleaning it up a bit.) This is a very small wall to scale for a thief though, and shouldn't be viewed as an end-all solution to the main problem.
Sadly, some people are evil. And they will continue to be evil.