In many cases, I could see this as being really annoying, but there are certain scenarios where a subtle background video using the HTML5
For more information, see MDN's entry on the HTML5 video element and Responsive HTML5/CSS3 Video Background by Ben Kaminski.
The sphere eversion video clip I use in the example can be found here. Also see Outside In on YouTube for those interested in learning more about Smale's paradox.