  We present a series of high-resolution cosmological simulations of galaxy
formation to z=0, spanning halo masses ~10^8-10^13 M_sun, and stellar masses
~10^4-10^11. Our simulations include fully explicit treatment of both the
multi-phase ISM (molecular through hot) and stellar feedback. The stellar
feedback inputs (energy, momentum, mass, and metal fluxes) are taken directly
from stellar population models. These sources of stellar feedback, with zero
adjusted parameters, reproduce the observed relation between stellar and halo
mass up to M_halo~10^12 M_sun (including dwarfs, satellites, MW-mass disks, and
small groups). By extension, this leads to reasonable agreement with the
stellar mass function for M_star<10^11 M_sun. We predict weak redshift
evolution in the M_star-M_halo relation, consistent with current constraints to
z>6. We find that the M_star-M_halo relation is insensitive to numerical
details, but is sensitive to the feedback physics. Simulations with only
supernova feedback fail to reproduce the observed stellar masses, particularly
in dwarf and high-redshift galaxies: radiative feedback (photo-heating and
radiation pressure) is necessary to disrupt GMCs and enable efficient coupling
of later supernovae to the gas. Star formation rates agree well with the
observed Kennicutt relation at all redshifts. The galaxy-averaged Kennicutt
relation is very different from the numerically imposed law for converting gas
into stars in the simulation, and is instead determined by self-regulation via
stellar feedback. Feedback reduces star formation rates considerably and
produces a reservoir of gas that leads to rising late-time star formation
histories significantly different from the halo accretion history. Feedback
also produces large short-timescale variability in galactic SFRs, especially in
dwarfs. Many of these properties are not captured by common 'sub-grid' galactic
wind models.
