Sometimes a common belief about search is just plain wrong. I've told lots of people that the videos found on Google Video (at video.Google.com) are a superset of the YouTube videos, and had them react with an "I didn't know that!"
(Okay. How many of you reading this far had that reaction?? Fess up now.)
The truth is that the videos on Video.Google.com are what Google finds by crawling the net, including video sites like YouTube.com, ABC.com, CBS.com, PBS.org, MySpace.com and so on.
The key thing to keep in mind is that YouTube is video that has been explicitly uploaded to YouTube.
Video.Google.com crawls all the video websites it can find, and gives links to those videos.
In a Venn Diagram:
Generally speaking, you'll find shorter clips of the premium content (think of shows like "Survivor" which exist only on CBS.com -- you can find clips and remixes of Survivor on YouTube, but can't get the whole show).
So when would you use Video.Google.com?
That's easy: Whenever you want to find full-length, professionally produced content and don't know where it exists. Since Video crawls other video sites, you can find out quickly where the original content exists, click through and watch in on the site. For example (to use Survivor again), if I don't know which channel produced the show, I'd just go to Google.com, search for [ survivor ] and click on the Video tab. I instantly find out that it was shown on CBS, and I can go there to watch it.
Since I rarely remember what production company or station has shown a particular show, this is a great way to figure out where it lives... and how to find it.