There has been only one time in my entire life where my two compasses did not agree, and I was at home and knew which direction was North when it happened.
But there are several other ways to confirm which compass is correct, assuming you are not standing upon a huge iron or nickel ore deposit, as Ted mentioned. Another mass of ferrous material which can sway a compass is your steel gun barrel, so be aware of that.
GLS already mentioned the use of an analog wrist watch (one with hands) to find direction, and I already mentioned the absolute reliability of both the sun and Polaris, the North Star... here in the Northern Hemisphere. Then there are other ways such as tracking the movement of the stars, sun, or moon through the sky over time due to the rotation of the earth. Less accurate, but still helpful is knowledge of the area you are hunting, which can help when you observe direction of water flow in rivers and streams. Moss doesn't always grow on the North side of trees, but it does most of the time in our hemisphere, and than can increase your directional odds. But I'd want to confirm that by using other means. Same for observing the amount of leaves on trees, since the heaviest growth is typically oriented toward the sun in the Southern sky.
I know guys who would never admit it, but they severely limit how far back in they will venture because they fear getting lost. Maps and a little knowledge of orienteering can really help your hunting by knowing where you are and where you want to go. A few trips through some steep ravines or large stands of multiflora rose, blackberry thickets, hawthorns, etc. will teach you in a hurry that the shortest distance between two points is not always a straight line. This can be especially true when it is dark and your flashlight is dead, or when you are dragging some dead weight like a deer.
