  Two entwined problems have remained unresolved since pulsars were discovered
nearly 50 years ago: the orientation of their polarized emission relative to
the emitting magnetic field and the direction of putative supernova ``kicks'
relative to their rotation axes. The rotational orientation of most pulsars can
be inferred only from the (``fiducial') polarization angle of their radiation,
when their beam points directly at the Earth and the emitting polar fluxtube
field is $\parallel$ to the rotation axis. Earlier studies have been
unrevealing owing to the admixture of different types of radiation (core and
conal, two polarization modes), producing both $\parallel$ or $\perp$
alignments. In this paper we analyze the some 50 pulsars having three
characteristics: core radiation beams, reliable absolute polarimetry, and
accurate proper motions. The ``fiducial' polarization angle of the core
emission, we then find, is usually oriented $\perp$ to the proper-motion
direction on the sky. As the primary core emission is polarized $\perp$ to the
projected magnetic field in Vela and other pulsars where X-ray imaging reveals
the orientation, this shows that the proper motions usually lie $\parallel$ to
the rotation axes on the sky. Two key physical consequences then follow: first,
to the extent that supernova ``kicks' are responsible for pulsar proper
motions, they are mostly $\parallel$ to the rotation axis; and second that most
pulsar radiation is heavily processed by the magnetospheric plasma such that
the lowest altitude ``parent' core emission is polarized $\perp$ to the
emitting field, propagating as the extraordinary (X) mode.
