You can now buy the iPhone 5c Dock or the iPhone 5s Dock, each of which costs $29. They are the first Apple-branded charge/sync docks for Lightning-connector devices.
The docks are only very slightly different, with the minor differences due to the minimally different shapes along the bottom of the new iPhone 5c and iPhone 5s. The iPhone 5s Dock will work with the original iPhone 5 as well. But neither dock will work if your iPhone is clad in a case—even Apple’s own cases.
The docks include a 3.5mm (1/4 inch) line out output. Apple’s website says that the docks will be available in stores beginning September 20.
Updated 9/11/13 to confirm that the iPhone 5s Dock works with the original iPhone as well.