A great, detailed post on the YouTube API blog from Google's YouTube team explains why they depend on the Flash Platform to deliver 2 billion videos a day to people worldwide.

First and foremost, we need all browsers to support a standard video format. Users upload 24 hours of video every minute to YouTube, so it's important to minimize the number of video formats we support. Especially when you consider that for each format, we also provide a variety of sizes (360p, 480p, 720p, 1080p). We have been encoding YouTube videos with the H.264 codec since early 2007, which we use for both Flash Player and mobile devices like the iPhone and Android phones. This let us quickly and easily launch HTML5 playback for most videos on browsers that support H.264, such as Chrome and Safari.

Concerns about patents and licensing have prevented some browsers from supporting H.264; this in turn has prevented the HTML5 spec from requiring support for a standard format. We believe the web needs an open video format option. One that not only helps address the licensing concerns, but is also optimized for the unique attributes of serving video on the web. To that end, we're excited about the new WebM project. Google is open sourcing and contributing the VP8 codec to the WebM effort. Google, Mozilla, and Opera have all committed to support WebM, and we have already started making YouTube videos available in the WebM format. Adobe has also committed to support VP8, the video codec for WebM, in an upcoming Flash Player release.

Robust video streaming - Closely related to the need for a standard format is the need for an effective and reliable means of delivering the video to the browser. Simply pointing the browser at a URL is not good enough, as that doesn't allow users to easily get to the part of the video they want. As we've been expanding into serving full-length movies and live events, it also becomes important to have fine control over buffering and dynamic quality control. Flash Player addresses these needs by letting applications manage the downloading and playback of video via Actionscript in conjunction with either HTTP or the RTMP video streaming protocol. The HTML5 standard itself does not address video streaming protocols, but a number of vendors and organizations are working to improve the experience of delivering video over HTTP. We are beginning to contribute to these efforts and hope to see a single standard emerge.