append_sid() was another function that really stood out when running phpBB profile data through Kcachegrind. On a viewtopic.php page it uses approx 20% of the page time. I've been able to reduce this to 10% by introducing this code at the top of the function:

        // Handle really simple cases quickly

        if ($_SID == '' && $session_id === false && empty($_EXTRA_URL) && !is_array($params))

        {

                return $url . ($params !== false ? '?'. $params : '');

        }

This covers the majority of calls to append_sid(). Call time can be further reduced to approx 6% by caching (static var) if there is a relevant hook available.