Add a class to panel page body element
You can use menu_get_item() to inspect what generated the page and add a class to the body element in template_preprocess_html(). I saw the code first in the Zen theme, where they also add a class if the page was generated by Views. Link to Zen template.php

    function MYTHEME_preprocess_html(&amp;$variables, $hook) {
      // Store the menu item.
      $variables['menu_item'] = menu_get_item();
      if ($variables['menu_item']) {
        switch ($variables['menu_item']['page_callback']) {
          case 'page_manager_blog':
          case 'page_manager_blog_user':
          case 'page_manager_contact_site':
          case 'page_manager_contact_user':
          case 'page_manager_node_add':
          case 'page_manager_node_edit':
          case 'page_manager_node_view_page':
          case 'page_manager_page_execute':
          case 'page_manager_poll':
          case 'page_manager_search_page':
          case 'page_manager_term_view_page':
          case 'page_manager_user_edit_page':
          case 'page_manager_user_view_page':
            // Is this a Panels page?
            $variables['classes_array'][] = 'page-panels';
            break;
        }
      }
    }