Two equivalent urls for YouTube are the following respectively for the normal and full size players:
http://www.youtube.com/watch?v=VideoID

Add parameters for this url adding &parameter=value&parameter=value&param...
 
http://www.youtube.com/v/VideoID

Add parameters for this url adding ?param=value&parameter=value&param....

High Definition: hd=1
Point in time autoplay: add '#t=1m32s' without the '?' (it's not a cgi param). you can also use the '#t=92s' format
 or ?start=92.
Autoplay: autoplay=1
Loop: loop=1
Hide search box: showsearch=0
Hide related videos: rel=0
Remove youtube branding: modestbranding=1
Hide title: showinfo=0