Loops through a bunch of videos (however many you want) and plays them infinitely. You can set the first one to "autoplay" in the markup if you wish. This uses jQuery but could be (should be) vanilla JavaScript easily enough. Doesn't work in IE8 or under (duh) because it uses addEventListener and uses the <video> element with no flash fallback.

vidLooper.js

vidLooper = function() {
  var allVids = $('.vid');
  $.each(allVids, function(index, value) {
    if (index < allVids.length-1) {
      value.addEventListener('ended', function() {
        var nextVid = allVids.eq(index+1);
        nextVid[0].play();
      });
    } else if (index === allVids.length-1) {
      value.addEventListener('ended', function() {
        var firstVid = allVids[0];
        firstVid.play();
      });
    }
  });
};