Understanding of Magento order statuses may be a bit challenging, so it was a pleasant surprise when I have found this nice graphic visualization from Aligent Consulting. See the diagram as embedded twit below. Click to the image to enlarge it.

not pretty, but I think our team has accurately sketched the #Magento order (not status!) state flow here pic.twitter.com/VoUDliuyRB — Aligent Consulting (@aligent) September 9, 2014

Couple notes from follow-up discussion in Twitter:

there maybe some differences with order statuses from version to version

A shipment can be created before an invoice which will also leads to the “Processing” state

For the additional reference here is a order workflow from official Magento CE 1.9 manual:

As you may notice, the diagram from Aligent Consulting provides more details about payment processing stage, which is quite important to know.