You'll see more changes coming up which will allow deeper customization of the embedded player -- whether you want the "classic" single video playback or some great new ways to display a variety of videos on your website, profile page or blog. Bottom line: we want this new feature on embeds to work for you.
If you'd like to turn off the option to see related videos through your embedded player, simply add "&rel=0" after the video ID number in the embed code. Here's an example of what your embed code should look like if you'd like to turn off this feature:
<object width="425" height="350"><param name="movie"
value="http://www.youtube.com/v/xxxxxx&rel=0"
></param><param name="wmode"
value="transparent"></param><embed src="
http://www.youtube.com/v/xxxxxx&rel=0"
type="application/x-shockwave-flash" wmode="transparent" width="425"
height="350"></embed></object>
Cheers,
YouTube Team