This paper presents the results of high-resolution N-body simulations that show dark matter halos in hierarchically clustering universes have a universal density profile, independent of halo mass, initial density fluctuation spectrum, or cosmological parameters. The density profiles of all halos can be accurately fit over two decades in radius using a simple formula originally proposed to describe galaxy clusters in a cold dark matter universe. The characteristic density of a halo is proportional to the density of the universe at the time it was assembled. A suitable definition of this assembly time allows the same proportionality constant to be used for all tested cosmologies. The results agree with previous studies on halo density profiles and show that the characteristic density and halo mass are strongly correlated. The paper also provides a step-by-step analytic procedure based on the Press-Schechter formalism to calculate equilibrium profiles as a function of mass in any hierarchical model. The results suggest that the density profile of an equilibrium halo can be specified by two parameters: halo mass and halo characteristic density. These parameters are related in such a way that the characteristic density is proportional to the mean cosmic density at the time when the mass of typical nonlinear objects was a fixed small fraction of the halo mass. The paper concludes that hierarchical clustering leads to a universal halo density profile, similar to the Hernquist profile, which is also observed in elliptical galaxies. The results suggest that the density profile of an isolated equilibrium halo can be accurately determined by giving two parameters: halo mass and halo characteristic density. The paper also discusses the implications of these results for the study of dark matter halos in different cosmological models.This paper presents the results of high-resolution N-body simulations that show dark matter halos in hierarchically clustering universes have a universal density profile, independent of halo mass, initial density fluctuation spectrum, or cosmological parameters. The density profiles of all halos can be accurately fit over two decades in radius using a simple formula originally proposed to describe galaxy clusters in a cold dark matter universe. The characteristic density of a halo is proportional to the density of the universe at the time it was assembled. A suitable definition of this assembly time allows the same proportionality constant to be used for all tested cosmologies. The results agree with previous studies on halo density profiles and show that the characteristic density and halo mass are strongly correlated. The paper also provides a step-by-step analytic procedure based on the Press-Schechter formalism to calculate equilibrium profiles as a function of mass in any hierarchical model. The results suggest that the density profile of an equilibrium halo can be specified by two parameters: halo mass and halo characteristic density. These parameters are related in such a way that the characteristic density is proportional to the mean cosmic density at the time when the mass of typical nonlinear objects was a fixed small fraction of the halo mass. The paper concludes that hierarchical clustering leads to a universal halo density profile, similar to the Hernquist profile, which is also observed in elliptical galaxies. The results suggest that the density profile of an isolated equilibrium halo can be accurately determined by giving two parameters: halo mass and halo characteristic density. The paper also discusses the implications of these results for the study of dark matter halos in different cosmological models.