  We present a detailed measurement of the proper motion of the Crab pulsar,
with the primary goal of comparing the direction of its proper motion with the
projected axis of its pulsar wind nebula (the projected spin axis of the
pulsar). We demonstrate that our measurement is robust and has an uncertainty
of only +/-0.4 mas/yr on each component of the proper motion. We find mu_alpha
= -11.7+/-0.4+/-0.5 mas/yr and mu_delta = +4.2+/-0.4+/-0.5 mas/yr relative to
the pulsar's standard of rest, where the two uncertainties are from the
measurement and the ncertainties in correcting the proper motion reference
frame, respectively. Comparing this proper motion to the symmetry axis of the
pulsar wind nebula, we must also consider the unknown velocity of the pulsar's
progenitor (assumed to be ~10 km/s), and hence add an additional uncertainty of
+/-2 mas/yr to each component of the proper motion, although this could be
significantly larger. This implies a projected misalignment with the nebular
axis of 14+/-2+/-9 degrees. We conclude that the precision of individual
measurements which compare the direction of motion of a neutron star to a fixed
axis will often be limited by fundamental uncertainties regarding reference
frames and progenitor properties. The question of spin-kick (mis)alignment, and
its implications for asymmetries and other processes during supernova
core-collapse, is best approached by considering a statistical ensemble of such
measurements, rather than detailed studies of individual sources. [abriged]
