I have not found a way to legally embed YouTube videos in PowerPoint 2013. As of February 2014, Microsoft’s Knowledge Base article says you can not do it. It currently lets you embed videos stored in your OneDrive account (assuming they are in one of PowerPoint’s supported formats) or on Facebook.
At this point, the only option I see for using a YouTube video legally in your PowerPoint 2013 is to put a hyperlink to it in your presentation. Clicking on the link during your presentation will open your default browser to the page with the video and begin playing it. Once the video is done playing, click back to your PowerPoint and resume the presentation.
While it is technically pretty easy to download a YouTube video (there are lots of tools/methods for doing so), it is generally not allowed. YouTube’s terms of service specifically says “You shall not download any Content unless you see a “download” or similar link displayed by YouTube on the Service for that Content.”
Hopefully, Microsoft and Google will work out their issues and make it easy for end users to utilize their products and services together (but I’m not holding my breath).