You need to use setTimeout() in this case because of how .delay() works (and your inability to cancel it).

$('.file a').live('mouseenter', function() {

  $.data(this, 'timer', setTimeout(function() {

      $('#download').stop(true, true).fadeIn('fast');

  }, 1000));

}).live('mouseleave', function() {

  clearTimeout($.data(this, 'timer'));

  $('#download').stop(true, true).fadeOut('fast');

});

You can give it a try here.

If you use .delay() it'll dequeue the next animation for the element, regardless of if you cleared that queue earlier. So you need a timeout that you can cancel, which the above does by manually calling setTimeout() and storing the result with $.data() so you can clear it later, via clearTimeout().