I had one on the 7/16 MCAT, although it could have been an experimental question. It's not too bad, here's how I do it.
Take your right hand and point your 4 fingers towards the first vector. Then bend your fingers towards the second vector (bend them in the way they normally bend, not a crazy contortionist configuration). The direction your thumb points is the direction of the cross product resultant vector. It will be perpendicular to both vectors, and its magnitude is the length of the two vectors multiplied by the sine of the angle between them (unlikely to be tested).
For example, East cross North is up (out of the map if you're looking down on one). West cross North is down (into the ground/map).
For North cross South the resulting product has a magnitude of zero, since these two vectors are parallel (sine of the angle between them = 0).