By default, Youtube suggests videos to viewers once a video has completed. It shows up in checkerboard form at the end of the video.
Example:

Screen Shot 2013-10-07 at 12.32.07 PM

Depending on what the previous viewers of the video have also watched, there may be videos suggested that may not be appropriate.

There is a way to prevent suggested videos from appearing at the end on a video in you blog.

Screen Shot 2013-10-07 at 12.40.50 PM
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Now when the video plays, suggested videos will not appear at the conclusion of the video.

Here is a great song that demonstrates the change.