First, the
geographic north pole -- where the latitude is exactly 90 degrees north -- is not the same as the
magnetic north pole -- the place to which the north pole of a compass points. (Indeed the geographic north pole doesn't even coincide exactly with the point through which the earth's rotational axis passes, I but I digress...)
The magnetic north pole wanders around a bit and is now located at a latitude about 83 degrees N & longitude 114 deg W. The difference between magnetic and geographic north is known as the magnetic declination, and must be taken into account if you're navigating by compass.
At the magnetic north pole, the magnetic field lines are vertical, i.e., perpendicular to the earth's surface. So if your compass is the traditional kind -- with a small bar magnet freely swinging on a pivot -- then directly over the magnetic north pole the compass's north pole will be attracted
downward and its opposite end (its south pole) will be repelled
upward. I hope this answers your question.
Since most compasses are not designed to allow this type of movement, it's hard to predict exactly how a compass will behave. There is no reason, however, to expect it to spin around as is sometimes wrongly believed or portrayed in cheesy movies.
Also note that since opposite poles attract, and given that the earth behaves roughly as if it's got a giant bar magnet stuck through it, then the earth's magnetic north pole -- which attracts the north pole of the compass's magnet -- physically is actually a south pole!
