Multiple level category drop-down

function parent_child_cat_select() { ?>
        <script type="text/javascript">
        /* <![CDATA[ */
            jQuery(document).ready(function() {     
                jQuery('#parent_cat').change(function(){
                    var parentCat=jQuery('#parent_cat').val();
                    // call ajax
                    jQuery.ajax({
                        url:"/wp-admin/admin-ajax.php",
                        type:'POST',
                        data:'action=category_select_action&parent_cat_ID=' + parentCat,
                        success:function(results)
                        {
                        jQuery("#sub_cat_div").html(results);
                        }
                     });
                });         
            });     
        /* ]]> */
        </script>

        <form action="<?php bloginfo('url'); ?>/" method="get">

        <div id="parent_cat_div"><?php wp_dropdown_categories("show_option_none=Select parent category&orderby=name&depth=1&hierarchical=1&id=parent_cat"); ?></div>

        <div id="sub_cat_div"><select name="sub_cat_disabled" id="sub_cat_disabled" disabled="disabled"><option>Select parent category first!</option></select></div>

        <div id="submit_div"><input type="submit" value="View" /></div>

        </form>
<?php }

function implement_ajax() {
    $parent_cat_ID = $_POST['parent_cat_ID'];
    if ( isset($parent_cat_ID) )
    {
        $has_children = get_categories("parent=$parent_cat_ID");
        if ( $has_children ) {
            wp_dropdown_categories("orderby=name&parent=$parent_cat_ID");
        } else {
            ?><select name="sub_cat_disabled" id="sub_cat_disabled" disabled="disabled"><option>No child categories!</option></select><?php
        }
        die();
    } // end if
}
add_action('wp_ajax_category_select_action', 'implement_ajax');
add_action('wp_ajax_nopriv_category_select_action', 'implement_ajax');//for users that are not logged in.

//this is optional, only if you are not already using jQuery  
function load_jquery() {
    wp_enqueue_script('jquery');            
}     
add_action('init', 'load_jquery');

For displaying the the drop-down menus use the parent_child_cat_select() function.

<?php parent_child_cat_select(); ?>