Not a rebuttal to Jeff Atwood's claim that copyright violation is the only reason anyone uses YouTube. Just several counterexamples I've seen in my own usage. Some of them do involve copyright infringement, but in unexpected ways, or ways which are obviously beneficial to the copyright holders.
1. Tutorial Videos
For instance, how to make a reece in Reason. I watched this, and found it very useful, although I think he leaves out an important step, which is adding a Subtractor with low sine wave oscillators to generate sub bass, which is ultimately even more essential to drum & bass basslines than texture. There are pages and pages of these things.
2. Weird Inventions
Particularly popular in the Ableton Live and Lego Mindstorms communities.
3. Actor Demos
I posted about "the iocaine powder defense" in Werewolf the other day. (As far as I can tell this a term Jim Weirch made up.) While googling for pictures of the actor who played Vizzini, I came across a kid re-enacting the entire scene. Although his "English accent" is a bit off, when he's playing Wesley/The Dread Pirate Roberts, he captured some of Vizzini's facial expressions with uncanny accuracy.
There's copyright infringement here, it's true, but it isn't the copyright violation Viacom's talking about, and nobody's going to make a YouTube re-enactment which outsells the original.
4. Funny Animals
Copyright infringement was the YouTube killer app for me, not too long ago. Then two things happened. First, Viacom got all the Daily Show clips taken down. For months I didn't go near YouTube. Second, the breakbeat producer Miyagi posted on a breakbeat discussion board that when he gets bored he googles YouTube for "funny animals." This just about changed my life.
5. Teenage Girls Dancing
I don't really understand this, but it's a whole subgenre. They usually can't dance, and they record the music with their webcams, so it sounds awful. I'm not saying it's a good use case, but it's certainly a popular one.
6. Music Videos & Just Music Itself
Like re-enactments, there is copyright infringement here, so technically it supports Jeff's argument, but the music companies never pull videos. They know it sells. Like re-enactments, a music video on YouTube is more likely to advertize a piece of music than to replace it.
7. Amateur Music Videos
Some of these involve copyright violation, some of them don't. Either way, they're very popular: people love music. In some cases these lead to CD sales.
Long story short, Viacom, by valuing their lawsuit at $1 billion - close to YouTube's $1.65 billion purchase price for Google - is asserting that most of YouTube's value comes from their content. I think Viacom - and the entertainment industry in general - does have a very argument to obtaining some portion of Google's advertizing income from YouTube clips made out of their material, whether remixed or not, but probably not as much as they think.
Update: bonus use case: making people think about Web 2.0. Michael Wesch's videos for the University of Kansas media literacy program are groundbreaking.