[ваый]

Ну у меня же работает.

<button>Load content</button>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.js"></script>
<script> 
$('.del-file').live({
    'click': function() {
       $(this).closest('.table-1-center').hide();
    }
});
 
$('button').click(function() {
    var html = '<div class="table-1-center"><span class="del-file">x</span></div>' + 
                    '<div class="table-1-center"><span class="del-file">x</span></div>';
    $('body').append(html);
});
</script>