// copyied from /wp-core/wp-includes/nav-menu-template.php > line 76 (wp 3.1.1) - start_el() function
$class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );

function wpse15319_check_nav_menu_classes( $classes )
{
    // You can take any of the $vars from the core function above: $classes, $item, $args
    echo '<pre>';
        // nice list:
        print_r( $classes );
        // or check of what type the $var is
        var_dump( $classes );
    echo '</pre>';

    return $classes;
}
add_filter( 'nav_menu_css_class', 'wpse15319_check_nav_menu_classes', 10 );

function wpse15319_add_nav_menu_classes( $classes )
{
    $classes[] = '';
    $classes[] .= 'my added css classes';

    return $classes;
}
add_filter( 'nav_menu_css_class', 'wpse15319_add_nav_menu_classes', 10 );