$(document).ready(function(){
    $('#addRow').live('click', function() {
        $('.leaderrow').clone().appendTo('#entries');
    });
})

<table width="100%" border="0" class="unsorted_table">
  <thead>
      <tr>
           <th>Name*</th>
           <th>Action</th>
      </tr>
  </thead>
  <tbody id="entries">
      <tr>
            <td>User's own name</td>
            <td>&nbsp;</td>
      </tr>
      <tr class="leaderrow">
            <td><select name="leaderid[]" >
              <option value="3">Sue</option>
              <option value="4">Jeannie</option>
              <option value="5">Kerry</option>
              <option value="6">Travis</option>
               </select>
            </td>
            <td><a href="" name="delete_row[]" class="remove">remove</a></td>
       </tr>
    </tbody>
    <tfoot>
       <tr>
            <td><p><input type="button" id="addRow" value="Add Another" /></p></td>
       </tr>
    </tfoot>
</table>

var tmpl = $(this).closest('table').find('.leaderrow.template');
tmpl.clone().removeClass('template').insertBefore(tmpl);
// and use CSS:
// .leaderrow.template { display: none; }