If your website or blog contains copy-right content in any page, AdSense will be removed when it Google AdSense people come to know of it in their automatic scrutiny or when someone complains.
Also if your site contains links to sites that are hosting copy right materials without permission, AdSense will be removed when it finds out in its scrutiny process or when a complaint is received.
This is a good policy to bring discipline in online world. I came across certain site expressly writing that people are not allowed to link to material in that site without permission. So AdSense publishers have to take note of this condition also. If a site prohibits linking, AdSense publishers can't link to that site. Normally sites encourage linking to get traffic to their sites. But there are some sites writing very clearly upfront that linking is not permitted.
Embedding of YouTube Videos
Many YouTube videos are not posted by their copy right owners but by others. AdSense publishers may have to be careful with this situation also. As a precaution, it will be prudent if only videos of YouTube partners are embedded. Some YouTube videos have prohibited embedding. There is no issue as you one can't embed them.
See content policies of AdSense
AdSense warnings and Expected Response