When you take the code youtube gives you to embed video on your webpage or website, at the end of the video related videos will be shown. This means it's more likely people will leave your website. To disable related videos on embedded youtube videos you just need to make two changes to the embed code:

In your embed code there will be two references to your video URL, like this:

http://www.youtube.com/v/DMxNkrwajN8

Append the following at the end of this link:

&rel=0

So working with the above example the link to our video in our object embed code would become:

http://www.youtube.com/v/DMxNkrwajN8&rel=0

When you make the above changes to the embed code and view your video, no related videos will be shown.

Easy peazy.