Does watching a YouTube video on another site leave you hungering for more like it? We just turned on a new embedded player with a scroll-through feature that shows related videos to your embeds. It's fun to play with and lets you discover new, related videos without leaving your site. Just hover over the video after pressing "play" and watch the magic unfold...
If for any reason you don't want this option turned on, you can modify the video URL by attaching a rel=0 parameter to the video. i.e. http://www.youtube.com/v/&rel=0
Here is an example of code with the parameter in place: