Assumes that your page depth is how the pages are organized in the page hierarchy, not custom menu hierarchy

add_filter('body_class','depth_body_class');
/**
 * Add page depth body class.
 *
 * Adds depth-x body class
 *
 * @author Jen Baumann
 * @link http://dreamwhisperdesigns.com/?p=1112
 */ 
function depth_body_class($classes) {
	global $post;
	if (is_page()) {
	    if ($post->post_parent)	{
        	$ancestors = get_post_ancestors($post);
			$depth = count($ancestors) + 1;
        } else {
        	$depth = 1;
        }
        $classes[] = 'depth-' . $depth;
	}
	return $classes;
}