As long as your phone is rooted, you can use the excellent Button Remapper app by appelflap as a convenient workaround. What the app will let you do is remap the camera button to work as the power button.
After installing the app, find the entry for "(Camera)" and set its Action to "Power" and its State to "WAKE_DROPPED". (WAKE tells the key to register even when the screen is off; WAKE_DROPPED does the same but drops the key before it is sent to the running application.) Optionally, remap the "(Power)" button to something innocuous like "Home" and set its state to "NONE" — that way, in case the real power button becomes active in a jammed state, the button input shouldn't mess up anything you are trying to do on the phone. After you are satisfied with your changes, click "Apply" to reboot the phone for the changes to take effect. In case you messed up, there will be a notification from Button Remapper in the status bar, which will let you reset any changes you have made.
Note that even when using Button Remapper to remap the hardware buttons, the remapping will not take effect when the phone is off (or you are booted into recovery mode). If your power button doesn't work, you will still have to use a workaround like plugging your phone into a charger in order to get the phone to power on from a shutdown state.
Seeing as how the power button design on the Motorola Droid appears to be partially defective (I know of at least a handful of Droid owners who have had the power button fail), on my replacement Droid I made the point of remapping the Camera button pre-emptively, in an attempt to minimize wear and tear on the power button. It's something to consider.