The solution: Try to keep your hands at waist level, right about where they might lightly brush your hip. Your arms should be at a 90 degree angle, with your elbows at your sides. You should rotate your arms at the shoulder (not at the elbow), so they're swinging back and forth.
Imagine a vertical line splitting your body in half -- your hands should not cross it. Keep your posture straight and erect. Your head should be up, your back straight, and shoulders level. When you're tired at the end of your run, it's common to slump over a little, which can lead to neck, shoulder, and lower-back pain. When you feel yourself slouching, poke your chest out.