Customer Placing the Largest Number of Orders


I think this can handle more than one numbers occurring the same number of max times:
SELECT customer_number FROM orders
GROUP BY customer_number
having count(distinct order_number) IN
(SELECT MAX(countn) FROM (select count(distinct order_number) as countn FROM orders GROUP BY customer_number) sub)

It can handle the case where more than one customer can have maximum number of orders.
SELECT customer_number FROM orders GROUP BY customer_number HAVING count(order_number) = ( SELECT count(order_number) FROM orders GROUP BY customer_number ORDER BY count(order_number) DESC LIMIT 1 )