Custom Order Number

or search frequently asked questions:

Will I be able to continue an existing numbering system?
Is it possible to use consecutive order numbers for different stores/views?
Can I customize order numbers on a store-view level?
Can I reset an order number counter on a regular basis?
Can I change numbers of already existing orders, invoices and shipments?
Can I add a suffix instead of a prefix?
Is it possible to make only the shipment number equal to the order number and leave invoice number unchanged?
Can I set a random number increment?
What happens with multiple invoices on one order?
What types of Magento order numbers are affected by this extension?