Using this blog as reference guide – perhaps slightly easier than bookmarking topics, and in case the internet eats the posts.

Per this thread, to delete an order, do the following:

SET @orderId = '100000001';

SET FOREIGN_KEY_CHECKS = 1;

DELETE FROM sales_flat_order
    WHERE increment_id = @orderId;
    
DELETE FROM sales_flat_quote
    WHERE reserved_order_id = @orderId; 

This works in Magento Community v 1.4.1.0 and Magento Enterprise 1.8.0.0. It deleted all mention of the order from the dashboard/reports.