fable666 - Not at all. That's why Youtube provides a share link and embed code, they want you to share videos and it's a great way to get good relevant content for your website and specific post if you do not want to create your own video.
What you CANNOT do is download a video from YT and republish it anywhere as your own. Unless it has a Creative Commons license. Those are videos that the creator of the video and Youtube have deemed as unprotected and can be downloaded and reused by a new creator anywhere, even within Youtube itself.
To find Creative Commons videos just select the filter option on the Youtube search results page and select Creative Commons, all the videos that show up in the search results now are free to use as your own
Hope that helps - Chef Mickey