It's also possible to have a YouTube video in your profile.
First, go to your favorite video on YouTube. It will be similar to this: http://www.youtube.com/watch?v=xA2lFXEZysc. Copy the video URL from your address bar, everything after the v=, which is here: xA2lFXEZysc and put it into bb-code like this: [youtube=xA2lFXEZysc].
To see if you have done it correctly, you can select the Preview button. If everything is as it should be, select Save.