Charge-neutral 180° domain walls that separate domains of antiparallel polarization directions are common structural topological defects in ferroelectrics. In normal ferroelectrics, charged 180° domain walls running perpendicular to the polarization directions are highly energetically unfavorable because of the depolarization field and are difficult to stabilize. We explore both neutral and charged 180° domain walls in hyperferroelectrics, a class of proper ferroelectrics with persistent polarization in the presence of a depolarization field, using density functional theory. We obtain zero temperature equilibrium structures of head-to-head and tail-to-tail walls in recently discovered ABC-type hexagonal hyperferroelectrics. Charged domain walls can also be stabilized in canonical ferroelectrics represented by LiNbO3 without any dopants, defects or mechanical clamping. First-principles electronic structure calculations show that charged domain walls can reduce and even close the band gap of host materials and support quasi-two-dimensional electron(hole) gas with enhanced electrical conductivity.