The potential use of the redshifted 21 cm line from neutral hydrogen for probing the epoch of reionization is motivating the construction of several low-frequency interferometers. There is also much interest in the possibility of constraining the initial conditions from inflation and the nature of the dark matter and dark energy by probing the power spectrum of density perturbations in three dimensions and on smaller scales than probed by the microwave background anisotropies. Theoretical understanding of the 21 cm signal has been fragmented into different regimes of physical interest. In this paper, we make the first attempt to describe the full redshift evolution of the 21 cm signal between 0<z<300. We include contributions to the 21 cm signal from fluctuations in the gas density, temperature, and neutral fraction, as well as the Lyα flux, and allow for a post-reionization signal from damped Lyα systems. Our comprehensive analysis provides a useful foundation for optimizing the design of future arrays whose goal is to separate the particle physics from the astrophysics, either by probing the peculiar velocity distortion of the 21 cm power spectrum, or by extending the 21 cm horizon to z≳25 before the first galaxies had formed, or to z≲6 when the residual pockets of hydrogen trace large-scale structure.