If you have having trouble embedding videos from Youtube or Vimeo on WordPress, make sure to check that you use http in the url and not https.
When I am writing this WordPress still does not support SSL (encrypted and secure communication), its a bug that has been reported a good while ago, and even with the latest WordPress version it still does not support https links.
To fix it, just change https to http in the link to the video.
So https://www.youtube.com/watch?v=QgKCrGvShZs only results in a text link, while http://www.youtube.com/watch?v=QgKCrGvShZs will embed the video, as you can see below.