We calculate the incoherent resonant and non-resonant scattering production of sterile neutrinos in the early universe. We find ranges of sterile neutrino masses, vacuum mixing angles, and initial lepton numbers which allow these species to constitute viable hot, warm, and cold dark matter (HDM, WDM, CDM) candidates which meet observational constraints. The constraints considered here include energy loss in core collapse supernovae, energy density limits at big bang nucleosynthesis, and those stemming from sterile neutrino decay: limits from observed cosmic microwave background anisotropies, diffuse extragalactic background radiation, and Li-6/D overproduction. Our calculations explicitly include matter effects, both effective mixing angle suppression and enhancement (MSW resonance), as well as quantum damping. We for the first time properly include all finite temperature effects, dilution resulting from the annihilation or disappearance of relativistic degrees of freedom, and the scattering-rate-enhancing effects of particle-antiparticle pairs (muons, tauons, quarks) at high temperature in the early universe.

24 pages, including 8 figures. v3: to match version in PRD, added references and numerous minor changes. High resolution color figures available at http://superbeast.ucsd.edu/~kev/nucdm