Exchange 2013 On-Premises and Exchange Online Hybrid Compatibility

We've had some questions come through to the Exchange Server and Office 365 teams regarding which versions of Exchange Online can be configured to work in a hybrid environment (where you have some mailboxes online and some in the cloud) with Exchange Server on premises. For example, does Exchange Server 2013 on premises work with the currently available version of Exchange Online? See the following table:

(See The New Exchange Reaches RTM! for more information regarding the new Exchange Server.)