The highest quality option on YouTube is currently 720p, but YouTube director of product management Hunter Walker announced at the NewTeeVee Live conference yesterday that they will start offering 1080p Full HD video next week.
Walk said the new resolution, as well as a new full-screen player, will roll out to all users within days.
YouTube co-founder Steve Chen announced high-quality YouTube viewing at NewTeeVee 2007. He also said, then, that YouTube stores all video it receives at the resolution it's uploaded at. So when YouTube ads a resolution option, as it did then and is doing now, it simply needs to re-encode videos for the new player, not get new raw content.
Walk said that about half of the 1080p content in the YouTube database has been re-encoded so far.