Apparently, YouTube has a few undocumented parameters that can effect the display of certain elements of an embedded player. I ran across this post in their developer forums following a request by a work associate to figure out how to hide the options displayed at the end of a played movie. Here is the list of known parameters along with the URL to the actual post:

• rel = 0/1 -> value for showing related videos
• color1 = hexadecimal color code -> value for the base color
• color2 = hexadecimal color code -> value for the over color
• border = 0…x -> value for the border width
• autoplay 0/1 -> value for automatically starting the video to play
• eurl = http://www.yourwebsite.com -> I believe this is the referring URL. Please correct me if I’m wrong.
• iurl = Path to the thumbnail image (I believe)

Custom URL parameters for YouTube embedded players