If you find the new player too cluttered and you want to use the old one, just append &rel=0 to the URLs from the code you have to include in your site. For example, http://www.youtube.com/v/UkguiR01gMQ should be replaced with http://www.youtube.com/v/UkguiR01gMQ&rel=0.
Garett Rogers from ZDNet thinks that YouTube prepares to include ads next to the related videos. "For the next several months, people will get very used to using the related video tool that was just introduced. As soon as it becomes second nature for users to use the tool, we should start to see sponsored results mixed with these related videos."
The new player didn't have too many fans because the related videos weren't always appropriate and sometimes they stayed in your way. "Thank goodness there's an option to turn it off, but it would be far better if it were off by default with an option to turn it on. I'm not so concerned as some other people about being presented links to potentially objectionable content (I can handle it like an adult), but having thumbnails pop up that do not disappear even if I mouse off of the video is a serious distraction and makes watching videos much less enjoyable," says a comment from YouTube's blog.
Probably as a reaction to the negative comments, the related videos are now visible only if you click on the "menu" button and at the end of the video.