We present a high-resolution X-ray image of SN 1006: a mosaic of four ROSAT HRI images that together cover the entire supernova remnant. A well-defined shock front is observed surrounding the remnant shell. Comparison of the X-ray and radio images shows a close correspondence in general morphology, especially for the brightest features. Along the northeast limb of the shell, where the remnant is brightest in both bands, the X-ray/radio correspondence is striking in its detail. The data are consistent with a model in which the X-ray emission in this region results primarily from synchrotron radiation by the same population of shock-accelerated electrons that produce the radio emission. New optical images show Ha emission over a much greater portion of the remnant than has previously been reported. Newly discovered faint filaments in the south, like the much brighter ones along the northwest limb, delineate the primary shock as it propagates into the interstellar medium. In the northwest, a narrow X-ray peak traces just inside the crisp optical filaments and provides a laboratory for observing the effects of a fast, nonradiative shock propagating nearly perpendicular to our line of sight. The calculated profile of the thermal X-ray emission from a rapidly ionizing postshock plasma closely matches the observed profile, supporting a model in which nonequilibrium thermal processes dominate the X-ray emission in the northwest. The measured displacement of 8 " between the optical filaments and the X-ray peak, combined with previously measured proper motions for the filaments, indicates a timescale of only similar to 120 yr for X-ray heating and ionization behind the shock. In addition to the narrow optical filaments around the rim of SN 1006, we find faint, diffuse H alpha emission within the remnant shell to the southwest. This emission probably represents nonradiative sheets viewed obliquely.