If a video hasn't been created by you, it obviously means that someone else owns the copyright on that video. The copyright owner has the right to give you permission to re-publish the video, or the right to deny you permission. If the owner desires, they can also allow you to re-publish the video, perhaps, only if you enter in to a certain royalty agreement with them.
However, when owners and creators of videos make them public on YouTube, they are given the option to either enable or disable the Share button for their videos. The Share button, when clicked, provides the HTML code that allows others to insert the video into their websites or blogs.
Therefore, if the owner enables the Share button, it simply means that they want others to embed the video, and in doing so, these videos may be freely embedded in any site. One would assume for the purpose of legitimate exposure