It's not quite an exact launch date, but Microsoft has announced that both Windows Server 2016 and System Center 2016 will launch at its Ignite conference (the successor to TechEd) this fall. Ignite runs from September 26-30 and is being held in Atlanta, Georgia.
Microsoft has also described how Windows Server 2016 will be serviced going forward. Full installations of the operating system—including the GUI and shell—will continue to be serviced on the "5+5" model that Microsoft has used for previous operating systems. That's five years of mainstream support, during which both bug fixes and feature improvements are made, and then five years of extended support, during which only security bugs will be fixed. The slimmed down Server Core installation will also be given this 5+5 servicing.
The new Nano Server option, however, will be handled in a different way. Nano Server installations will be updated more or less in tandem with the Windows 10 Current Branch for Business (CBB) release. CBB trails the main consumer branch by about six months, giving new features a bit of time to receive some real-world testing before being distributed to more conservative organizations. CBB is expected to be updated two to three times a year, and this will apply to Nano Server deployments of Windows Server 2016 just as it does to CBB deployments of Windows 10.