Linking directly to a high definition (HD) version of a YouTube video used to be done by adding "&fmt=" and 35, 22, or 37 at the end of the link. This no longer works, but you can still use "&hd=1", which will link to the 720p version of a video, if available. Here is an example of a link with "&hd=1" added to the end of it:
The following will also work:
Thanks to commentor KarDave for pointing out that you can link directly to the popout version of a 1080p video. It won't be in the normal YouTube layout and will be just the video at full browser dimensions. The link is:
http://www.youtube.com/watch?v=cvt08Tvcyw4&hd=1
The following will also work:
http://www.youtube.com/watch?v=cvt08Tvcyw4&feature=related&hd=1
Thanks to commentor KarDave for pointing out that you can link directly to the popout version of a 1080p video. It won't be in the normal YouTube layout and will be just the video at full browser dimensions. The link is:
http://www.youtube.com/watch_popup?v=VIDEO_ID&vq=hd1080
Replace VIDEO_ID with the ID of the video, naturally. If you leave the &vq=hd1080 out, or the video does not support 1080, it will default to 720 (if available). You can also use 3rd party embedded players to have more control over the playback, but that won't be covered here.
Youtube Version 3 Player(New Palyer) With Full HD Embed Code
<iframe class="youtube-player" type="text/html" width="640" height="385" src="http://www.youtube.com/embed/VIDEO_ID&vq=hd1080&version=3&hl=en_US" frameborder="0">
</iframe>