Unpairing an already-paired Apple wireless keyboard

Solution 1:

Try resetting your keyboard as explained here and here:

1. Turn off the keyboard; better yet, remove the batteries.
2. Click the Bluetooth icon in the upper toolbar, then select “Set Up Bluetooth Device”. If you don't see this icon on your toolbar, click on your System Preferences in the dock, and then Bluetooth in that menu.
3. Wait for the Bluetooth Set Up Assistance to come up and start searching for devices.
4. Insert the batteries and HOLD the power button. Do NOT let go until step 7.
5. Your keyboard should now appear in the assistant.
6. Select the keyboard from the list and click Continue, while still holding the power button.
7. Once you get the pairing code, let go of the power button and type in the code.

For more information on pairing, see Set up your Apple wireless devices at Apple Support.

Solution 2:

The accepted answer does not work with the latest OSX (El Capitan). Here are the updated instructions.

Firstly lets all acknowledge, this is not Apple's finest moment in user experience engineering. Onwards.

The Apple bluetooth keyboard is infuriating because the little green light doesn't give you enough information to indicate if it is turning off because battery is dead or for other reasons. So you're a bit blind if the batteries are dead, but otherwise the following instructions should work.

1. Go to System Preferences, then Keyboard
2. Set Up Bluetooth Keyboard...
3. Hold down the power button of the keyboard (the one on the tube, on the right side, not the power button key on the top right of the keyboard).
4. If you hold it down for 4 or 5 seconds, the setup panel will change from "No keyboard found" to "keyboard found". Don't let go of the button!
5. Now here is the key step. While still holding down that power button, don't let it go, you need to use your mouse to press "Next" on the dialog.
6. Connected.