We present images of the Crab synchrotron nebula obtained with the Wide Field and Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope. These data are compared with ROSAT HRI images, and with 0."5 resolution Canada-France-Hawaii Telescope (CFHT) images previously published by van den Bergh & Pritchet (1989). These data strengthen the emerging picture of the Crab as a cylindrically symmetrical object with an axis running southeast to northwest, and inclined by ̃20°-30° with respect to the plane of the sky. Identification of structure very near to the pulsar which shares this symmetry helps to better establish the link between the symmetry axis of the nebula and the spin axis of the pulsar.We report the discovery of a bright knot of visible emission located 0."65 to the southeast of the pulsar, along the axis of the system. This knot and a second knot 3."8 from the pulsar appear to be present but not well resolved in the 1988 CFHT image, indicating that they are persistent structures. The inner knot is interpreted as a shock in the pulsar wind ̃1500 AU above the pole of the pulsar. No corresponding knots are seen to the northwest of the pulsar, which may indicate that the characteristics of the wind from the two poles are not symmetrical. The closest of the "wisps" to the northwest of the pulsar appear to close into a ringlike "halo" encircling the axis of the nebula. The wisps are resolved, with widths of ̃0."2. This allows calculation of their volumes and volume emissivities, and in turn their equipartition fields and pressures. Equipartition pressures calculated for the knots and wisps are typically 10 to as much as 80 times the equipartition pressure calculated for the nebula as a whole. The wisps show significant substructure which changed considerably between 1988 and 1994. Previous reports of relativistic motions of the wisps were probably due to changes in the unresolved substructure of these features. Comparison of the CFHT and WFPC2 images show remarkable changes in the inner nebula, but inferences about physical conditions based on this comparison are limited by the resolution of the CFHT data and the long 5 year baseline between the images. The structure of the nebula in 1994 may be inconsistent with the recent model by Gallant & Arons (1994). Very fine fibrous texture visible in the WFPC2 image follows the structure of the X-ray torus. A puzzling anticorrelation is seen between the X-ray and visible surface brightness through part of the torus. Long contiguous low contrast features with widths of ̃1"-2" are seen to run throughout the volume of the nebula. These features are seen to move outward through the nebula at velocities in excess of homologous expansion. These features trace the magnetic structure of the nebula; they are probably due to differences in emissivity accompanying varying degrees of departure from equipartition at roughly constant total pressure. Visible fibers "drape over and appear to expand away from an X-ray counterjet to the northwest of the pulsar, supporting the interpretation of the counterjet as a directed flow of energy along the symmetry axis of the nebula. Other associations are also seen between X-ray and visible structures, including X-ray emission surrounding the east and west bays. An association is proposed between the observed structure of the nebula and different latitude zones found in models of winds from partially oblique rotators. We concur with previous suggestions that the X-ray torus and the sharp visible fibers associated with it mark a shock at rs ̃ 1.2 × 1018 cm in an equatorial striped magnetic wind. The halo and anvil arise at a distance of ̃1.4 × 1017 cm from the pulsar in a helically polarized wind at latitudes greater than about 35°. Well collimated polar jets may be responsible for the knots to the southeast of the pulsar and for the jet and counterjet seen at X-ray and visible wavelengths.