Reposicionando elementos usando JQuery

Copie este código para sua página de testes e execute a página.

<style>
 #sortable { list-style-type: none; margin: 0; padding: 0; width: 60%; }
 #sortable li { margin: 0 3px 3px 3px; padding: 0.4em; padding-left: 1.5em; font-size: 1.4em; height: 18px; }
 #sortable li span { position: absolute; margin-left: -1.3em; }

</style>

<script>
 $(function() {
  $( "#sortable" ).sortable();
  $( "#sortable" ).disableSelection();
 });

</script>
<div class="demo">
<ul id="sortable">
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 1</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 2</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 3</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 4</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 5</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 6</li>
<li class="ui-state-default"><span class="ui-icon ui-icon-arrowthick-2-n-s"></span>Item 7</li>
</ul>
</div>
<div class="demo-description" style="display: none;">
Enable a group of DOM elements to be sortable. Click on and drag an element to a new spot within the list, and the other items will adjust to fit. By default, sortable items share <code>draggable</code> properties. </div>

Fonte: http://jqueryui.com/demos/sortable/