How do I add a body class to specific pages?

add_filter('body_class','cp_new_body_classes');
function cp_new_body_classes($classes) {
    if( !is_page_template() )
        $classes[] = 'reg-page';

    return $classes;
}

The problem was that you are only returning the classes if !is_page_template(), but you want to return the classes always as it contains the other classes you didn’t add yourself in an array, you just want to add some then return them like normal.