There are a few methods suggested for doing this online, but none of them seem to work.
For example:
http://blog.makezine.com/archive/2008/11/youtube-in-720p
The first example below does not work for me, but the second one does (in Chrome).
I believe the first one uses the new HTML5 youtube player whereas the bottom one (which works) uses the older flash player. However, the second one doesn't seem to load correctly in Safari/Firefox etc so probably not usable.