Zidan_@777@, 
условие не читал что ли?
$brth = mysql_result(mysql_query("SELECT COUNT(*) FROM `users` WHERE `dayb` = '" . $day . "' AND `monthb` = '" . $mon . "' AND `preg` = '1'"), 0);
if ($brth)
echo '<div class="menu"><a href="str/brd.php">Именинники</a> (' . $brth . ')</div>';