MediaElements.js is an open source jQuery-based project (which I use and like) which allows you to use HTML5 video and audio in any browser all the way back to IE 6. It tests if the browser supports HTML5. If yes, it uses that. If no, it falls back to displaying the media through Silverlight or Flash. Regardless of what it uses, the UI is always consistant.
Now available as a WordPress plugin to make it even easier. Just use simple shortcodes to link up the video and specify what options you want (e.g. autoplay, fullscreen, etc).