Actually, I made my own Youtube BBcode for my own forum. It's not all done yet but
CODE
<object width="560" height="340">
<param name="movie" value="http://www.youtube.com/v/{SIMPLETEXT}&fs=1&rel=0&color1=0x006699&color2=0x54abd6&hd=1"></param>
<param name="allowFullScreen" value="true"></param>
<param name="allowscriptaccess" value="always"></param>
<embed src="http://www.youtube.com/v/{SIMPLETEXT}&fs=1&rel=0&color1=0x006699&color2=0x54abd6&hd=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="560" height="340"></embed>
</object>
And the BBCode itself
CODE
[Youtube]{SIMPLETEXT}[/Youtube]
You can use this code if you have your own forum.
It is made for the phpBB 3 forum but it can be easily changed if your forum uses something else.
To post a video, all you need to do is have the part
http://youtube.com/watch?v=UY0xwRIGOdc inside a [youtube] tag so
CODE
[youtube]UY0xwRIGOdc[/youtube]
EDIT: Just Finished it
CODE
<div style="padding:5px;width:640px;text-align:center;-moz-border-radius:4px;-webkit-border-radius:4px; background: #CCCCFF; border: double #9999CC">
<center><h2>{SIMPLETEXT1}</h2></center>
<embed src="http://www.youtube.com/v/{SIMPLETEXT2}&rel=1&fs=1" type="application/x-shockwave-flash" allowFullScreen="true" allowScriptAccess="never" wmode="transparent" width="640px" height="385px"></div>
BBCODE
CODE
[youtube="{SIMPLETEXT1}"]{SIMPLETEXT2}[/youtube]
Anyone may use this. I made the colors for that it would fit in on R3.