X-ray pulsars are the only accreting magnetic stars where rotation torques induced by accretion are large enough to be measured on short timescales ~ days. They are thus unique laboratories for studying the interaction between an accretion disk and a stellar magnetosphere. We describe 5 years of continuous pulsar timing observations by the BATSE instrument on GRO which paint a strikingly different picture of pulsar spin behavior than understood from the previous 20 years of sparse observations. In particular, we find that more than half of the persistent pulsars we observe undergo dramatic torque reversals, switching suddenly between extended periods of steady spin-up and steady spin-down. Moreover, variations in pulsed flux are anticorrelated with torque in at least one system undergoing secular spin-down, GX1+4. This behavior contradicts standard accretion torque theory (Ghosh and Lamb 1979). A simple – albeit unconventional – hypothesis which naturally explains these observations is that the disks in these systems somehow alternate between epochs of prograde and retrograde rotation.