I dropped my crystal ball in the toilet while taking a call on my 1-900 line last night, so I can't get a reading for you over here.
Seems like sending units are usually the culprit, but I have had a bad connection between the gauge and the contact/clips in the back of the instrument cluster at least once. The voltage to the gauge remains constant, and the reading is extrapolated from the sending unit varying resistance to ground as oil pressure changes... I can't remember the exact resistance range, but I think it's 0-90 ohms. A quick test to determine if the gauge and wiring are likely okay is to unplug the wire from the sending unit then get the reading on the gauge with the wire disconnected, then see what it says when you ground the wire. The gauge should go off the far end of the scale and point to about 3 o'clock with the wire disconnected, then read exactly 0 when you ground it.
You do mean that the gauge is not reading zero with the key on and the engine not running, right? As with the temperature and fuel gauges, the oil pressure gauge won't return to zero when you switch the ignition off; usually the needle will just stop right where it was at when you turned the ignition off, though they occasionally drift around when not powered up, too.