Whether supernovae are major sources of dust in galaxies is a long-standing debate. We present infrared and submillimeter photometry and spectroscopy from the Herschel Space Observatory of the Crab Nebula between 51 and 670 mu m as part of the Mass Loss from Evolved StarS program. We compare the emission detected with Herschel with multiwavelength data including millimeter, radio, mid-infrared, and archive optical images. We carefully remove the synchrotron component using the Herschel and Planck fluxes measured in the same epoch. The contribution from line emission is removed using Herschel spectroscopy combined with Infrared Space Observatory archive data. Several forbidden lines of carbon, oxygen, and nitrogen are detected where multiple velocity components are resolved, deduced to be from the nitrogen-depleted, carbon-rich ejecta. No spectral lines are detected in the SPIRE wavebands; in the PACS bands, the line contribution is 5% and 10% at 70 and 100 mu m and negligible at 160 mu m. After subtracting the synchrotron and line emission, the remaining far-infrared continuum can be fit with two dust components. Assuming standard interstellar silicates, the mass of the cooler component is 0.24 super(+0.32) sub(-0.08) M sub(middot in circle) for T = 28.1 super(+5.5) sub(-3.2) K. Amorphous carbon grains require 0.11 + or - 0.01 M sub(middot in circle) of dust with T = 33.8 super(+2.3) sub(-1.8) K. A single temperature modified blackbody with 0.14 M sub(middot in circle) and 0.08 M sub(middot in circle) for silicate and carbon dust, respectively, provides an adequate fit to the far-infrared region of the spectral energy distribution but is a poor fit at 24-500 mu m. The Crab Nebula has condensed most of the relevant refractory elements into dust, suggesting the formation of dust in core-collapse supernova ejecta is efficient.