How many YouTube videos are there?

Around 797 million.

As of February 2010, typing the string ‘Å“site:www.youtube.com/watch’ on Google returns more than 797 million search results. This means that there are more or less 797 million videos posted on YouTube. In February 2006 YouTube announced that 65,000 videos were uploaded to the site daily; in 2008 Google claimed that 13 hours of video are uploaded to YouTube per minute.