Full screen (background) video with just CSS: http://jsbin.com/EzakOYIb/1

full-screen-video.css

.full-screen-video-container{
  position: absolute;
  left: 0;
  right: 0;
  top: 0;
  bottom: 0;
  overflow: hidden;
}
.full-screen-video-container video{
  position: absolute;
  left: 50%;
  top: 50%;
  -webkit-transform: translateX(-50%) translateY(-50%);
  -ms-transform: translateX(-50%) translateY(-50%);
  transform: translateX(-50%) translateY(-50%);
  min-width: 100%;
  min-height: 100%;
}

full-screen-video.html

<div class="full-screen-video-container">
  <video autoplay="autoplay" loop poster="http://media.w3.org/2010/05/bunny/poster.png">
    <source id="mp4" src="http://media.w3.org/2010/05/bunny/movie.mp4" type="video/mp4">
    <source id="ogv" src="http://media.w3.org/2010/05/bunny/movie.ogv" type="video/ogg">
    <p>Your user agent does not support the HTML5 Video element.</p>
  </video>
</div>