While Microsoft and Google continue to bicker about an official YouTube app, back in the real world I see no reason why everyone who would watch online video on their Windows Phone handset wouldn't already be using this app from LazyWorm. It gives you full access to your YouTube account, favourites, subscriptions, the higher resolution YouTube videos, and all the metadata from each video.
It also allows other third party apps to use MetroTube to play back Youtube videos, rather than going through the Windows Phone web browser, through the use of the URI scheme available in the Windows Phone SDK.
You can find MetroTube in the AAWP App Directory.