This is just a quicky because I have noticed a lot of people struggling with it, including some of the admin group.
1) The link can't be the short version that you can grab under the share tab.
i.e. http://youtu.be/7N28FRdCs3k
2) You can't have any embed or playlist data afterwards.
i.e. https://www.youtube.com/watch?v=7N28FRd ... 0C94BE62E8
3) The link cannot be an https link, I have noticed that this has been the most common problem.
i.e. https://www.youtube.com/watch?v=7N28FRdCs3k
4) The can't be a mobile link.
i.e. http://m.youtube.com/watch?v=7N28FRdCs3k
5) If you follow these and get a link that follows the rules, it should work.
i.e. http://www.youtube.com/watch?v=7N28FRdCs3k
6) If you now put it into the youtube BBCode tag you'll get your embed.
i.e.