Mean pulse shape and polarization parameters have been obtained for PSR J0437-4715 at 438, 660, and 1512 MHz using the Australia Telescope National Facility Parkes 64 m radio telescope and the Caltech correlator. The pulse profile is complex with many identifiable features, including an unusual double "notch," and evolves strongly with frequency. Strong linear and circular polarization are observed at all frequencies, with the fractional linear polarization highest near the wings of the pulse. Circular polarization is strongest near the pulse center, with a sense reversal at the center. Position-angle variations are complex and include what appear to be orthogonal-mode transitions. However, at other frequencies, some of these transitions are not orthogonal. Even when these transitions are allowed for, the position angle does not follow the simple rotating-vector model, suggesting departures from a dipole field configuration in the emission region. A frequency-dependent lag of the total-intensity profile with respect to the polarization profile is observed. This effect has not previously been seen in any pulsar. An improved value of the rotation measure along the path to the pulsar is derived.