From the developers PDF letter to customers:
We are extremely saddened to announce that as of the 1st of January 2012, our applications ‘Metrotube’ and ‘YouTube’ will no longer be available for download from the Windows Phone Marketplace. YouTube’s current API does not have any documented methods for obtaining high quality video content. We have been using a workaround to obtain this content and it has recently come to our attention that this may not be sustainable in the long term, hence our decision to stop distributing the apps. The apps should remain functional for those who have already installed them however we will be unable to push out any further updates. Of course, you can also continue accessing YouTube videos directly through your web browser.
The root cause of all this is between Google and Microsoft, and access to the "extra" bits of metadata to make a really good YouTube client. In the meantime, Windows Phone users will need to find another 3rd party party client come the New Year (or when they have to hard reset their phones and lose all the installed apps).