Strongly magnetized neutron stars are believed to underlie a variety of astrophysical systems, although conflicting observational and theoretical evidence has led to debate on the origin and stability of these magnetic fields. Here we describe a new model of neutron star magnetic moments, assuming that the fields are generated at birth and following their evolution to ages as large as the Hubble time. With realistic thermal evolution and conductivities, isolated neutron stars will maintain large magnetic dipole fields. As suggested elsewhere field modification under mass accretion might lead to torque decay. We identify an operative mechanism for this process; the results of this unified picture are in agreement with observations of a wide range of neutron star systems.