The good news is that you can download the captions file if you know the URL: http://video.google.com/timedtext?lang=en&v=VIDEO_ID, where you should replace VIDEO_ID with the ID of the YouTube video. Here's the captions file for Eric Schmidt's keynote.
It's an XML file and you can extract plain text by removing all the tags. Right-click on the page, select "view source", copy all the text and paste it on this page.
Now it's easy to copy an excerpt from the keynote:
We have one of the largest databases of information in the world which we've engineered and which is very, very difficult technologically in order to house all that information and ready for more. So, where do we go next with search? Well, you've got personal contacts, personal emails, personal network of people and your relationships with them, and with your permission -- and I need to say that about 500 times -- with your permission, we can actually search and index that information and make all of these answers so much better. The next step after that is obviously autonomous search. This is searches that you're -- that are occurring while you're not even doing searching.