The [protocol relative][1] source URL isdoes not correctwork. Try:
<apex:page >
<apex:iframe width="854" height="510" src="https://www.youtube.com/embed/SGPvYQ1o2x4" frameborder="0"/>
</apex:page>
-Answer edited to incorporate Keith C's comment [1]: http://billpatrianakos.me/blog/2013/04/18/protocol-relative-urls/