Licence for including (with HTML embed tag) others YouTube videos
If you use the YouTube embed feature then it is allowed according to the YouTube terms of service. If the uploader doesn't want their video to be embedded they can simply turn it off in the video manager.  

What is not allowed, whether the embed feature is enabled or not, is that you rip the video from YouTube and then distribute it from your own servers. The only exception is that the video author gave you permission to do this. 

Also, you may get a cease and desist letter if you have a habit of just putting a ton of YouTube videos on your webpages and some ads and no original content of your own.