In many of our projects, we embed YouTube videos as part of the site content. By default, when a YouTube video finishes playing, it shows a bunch of related videos, which unfortunately can be VERY unrelated.
To avoid showing any related videos, please include "rel=0" parameter with the YouTube URL in the embed code. Or, just unchecked the option when you get the embed code from YouTube.
This is something we should always do to save ourselves and our clients from potential embarrassing situations.