The reason tags are restricted to a certain set is to lessen the chance of evil code being implanted into your site. That said, all you need to do is add the tags for the type of video you want to allow. So for YouTube, you would add the following code to your Allowed Tags:
object => (width => () height => ())
param => (name => () value => ())
embed => (src => () type => () allowfullscreen => () width => () height => ())
Then you could add the following embed code to an image description to display a YouTube video.
<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/SSfccjd1bdU&hl=en&fs=1"></param><param name="allowFullScreen" value="true"></param><embed src="http://www.youtube.com/v/SSfccjd1bdU&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" width="425" height="344"></embed></object>