A patent Apple filed in July 2011 has become public and in case all the rumors weren't enough, this one states that Apple is registering a "wrist-worn electronic device."
Unlike previous speculation that it would be called the "iWatch," this filing includes drawings which say "iTime." Still, considering Apple has given the public no information about the device or its name, and this was filed in 2011, there is no guarantee it will be called either of those names.
In U.S. Patent 8,787,006, Apple states "the invention pertains to an electronic wristwatch," but it doesn't give away much more than that.
The drawings show buttons, as expected, on the front and side of the devices, as well as what appears to be a headphone or charging jack. The patent also allows for sensors to control the device via gestures. In the patent, Apple writes,
For example, the gesture might be a horizontal movement for one user input option (e.g., decline incoming call), and might be a vertical movement for another user input option (e.g., accept incoming call). For example, the gesture might be a single shake (or bounce, tap, etc.) of the user’s wrist for one user input option (e.g., accept incoming call), and might be a pair of shakes (or bounces, taps, etc.) for another user input option (e.g., decline incoming call).
While this certainly points us further in the iWatch (or iTime) direction, this does not tell us too much about the actual functionality or design of the watch. We will have to wait till Tim Cook is ready to spill the iBeans for that.