You know when you watch a video on Youtube there are recommendations that follow it? Well you can turn those recommendations off if you want.
There are two easy ways to use Youtube as a hosting platform for your videos, either the older 'embed' style code or the newer 'iframe' code. Both of these contain a URL from you site to Youtube, pulling the video in by a unique id.
All you have to do to stop the 'after-video' recommendations is to add a simple url parameter to the Youtube reference. Append this to the end of the URL string.
I'm guessing it means 'related = false', i.e. don't show related videos. Note that it also removes the 'like' and 'dislike' options as well.
You can try it out with the Skyrim trailer below.