How to Turn Off Search and Related Videos Using YouTube on My Site
The short answer is add &rel=0 to the last youtube url in the flash embed code they give you for posting to your blog, affiliate promo page, optin page, salesletter or whatever.
i.e.
<embed src="http://www.youtube.com/v/q4lVvyBpVcs&hl=en&fs=1&rel=0"
hth,
big jason