Appending a GET-Variable to wp_nav_menu

Filter 'wp_nav_menu_objects'. You get an array as argument, a list of all items.

Pseudo-code, not tested:

add_filter( 'wp_nav_menu_objects', 'wpse_76401_filter' );

function wpse_76401_filter( $items )
{
    $out = array();
    foreach ( $items as $item )
    {
        if ( isset ( $item->url ) )
            $item->url = add_query_arg( 'variable', '123', $item->url )

        $out[] = $item;
    }

    return $out;
}