Colin, the transformer idea, suggested in the above post, is most likely is a no-go, since transformers only work on alternating currents.
If, as you suggested, a resistor is used, that wouldn't work neither, since all the resistor does is reduce the flow of current - not voltage. My guess would be that the actual stepping-down of the voltage is carried out inside the navigator itself... usually in the form of an on-board (+5v) regulator.
I could be out of my depth here, but my take is that your 12v adaptor is just a straight-through 12v-to-12v connector. If you have access to a multi-meter, try measuring the output voltage -- it's possible the output will be at the same potential as the input.
The only resistor inside the adaptor would be the one limiting the current to that green LED.
Leaving the adaptor 'live' should cause no harm at all.
If, on the other hand, the output of your adaptor *is* lower than the the input, then it would appear that the regulator is inside the adaptor -- not the navigator. If this is the case, when you remove the nav' from the car, the regulator gubbins inside the adaptor would only be pulling a few measly milliamps anyway.... hardly enough to threaten premature discharge of your car battery.
Either way, I would say that it's safe if you need to leave it permanently plugged in.
However, I'd take a couple voltage readings with the multi-meter first, just to be certain.