At 7:00 a.m. PDT I was heading for my video page on YouTube and ran into this message:
I was getting to other sites just fine, so it's safe to assume it's a Google problem. YouTube receives 10 hours of video per minute and is by far the leader in the crowded field. This provides another example of why the Internet isn't like television, which tends to have higher uptime but the content just isn't as interesting as what you can find on YouTube. Awaiting word from Google on this topic.
Update: As of 7:20 a.m. YouTube has been revived.
Allen Stern at CenterNetworks has some more detail.