There exist magnetic fields in which particles bouncing between mirror points experience no net first-order guiding center drift. In such fields, even though the instantaneous gradient and curvature drifts are not zero, their total effect integrated over any bounce period vanishes, so that particles merely wobble back and forth around fixed field lines. A class of two-dimensional drift-free fields, somewhat resembling the configuration found in the geomagnetic tail, is described; several proofs of the drift-free property are given, including some that suggest that the property of vanishing net drift might extend to nonadiabatic orbits. A general criterion for identifying drift-free fields is developed, and a case of motion in a nearly drift-free field is also investigated. The theory is applied to the plasma sheet in the earth's magnetotail, and observational evidence is presented suggesting that the magnetic field there indeed approaches a drift-free configuration.