YouTube Adds Related Videos To Embedded Players
So view the related videos, just mouse over the video as it is playing on your browser. You will then see a Mac dock genie like affect in the video, that shows related videos. If you do not want related videos to show up, you can simply add rel=0 to the URL parameter of the code. Examples can be found at the YouTube blog.
Postscript: YouTube has now changed how they handle displaying the related videos. To now see related videos, you must click on the “menu” button. Before, all you had to do was mouse over the video. More details on this change at Google Blogoscoped.