The 30-Hz rotation rate of the Crab pulsar has been monitored at Jodrell Bank Observatory since 1984 and by other observatories before then. Since 1968, the rotation rate has decreased by about 0.5 Hz, interrupted only by sporadic and small spin-up events (glitches). 24 of these events have been observed, including a significant concentration of 15 occurring over an interval of 11 yr following MJD 50000. The monotonic decrease of the slowdown rate is partially reversed at glitches. This reversal comprises a step and an asymptotic exponential with a 320-d time constant, as determined in the three best-isolated glitches. The cumulative effect of all glitches is to reduce the decrease in slowdown rate by about 6 per cent. Overall, a low mean braking index of 2.342(1) is measured for the whole period, compared with values close to 2.5 in intervals between glitches. Removing the effects of individual glitches reveals an underlying power-law slowdown with the same braking index of 2.5. We interpret this value in terms of a braking torque due to a dipolar magnetic field in which the inclination angle between the dipole and rotation axes is increasing. There may also be further effects due to a monopolar particle wind or infalling supernova debris.