They do: use this one.
http://www.airbus.com/en/corporate/orders_and_deliveries/#

It is very useful and has all orders and deliveries to date. Please tell me if Boeing has similar information available.

They do indeed.

Also, you can call up a personal search for deliveries. You can find out how many 707s, for example, where delivered between 1960 and 1961, if that interests you.