Vapor-liquid coexistence in fluids of charged hard dumbbells, each made up of two oppositely charged hard spheres with diameters sigma and separation d, has been studied using grand-canonical Monte Carlo simulations. In the limit d/sigma-->0, and with the temperature scaled accordingly, the system corresponds to dipolar hard spheres. For separations in the range 0.3<d/sigma<or=1 the coexisting vapor phase contains compact clusters. For separations in the range 0.1<or=d/sigma<0.3 the coexistence is between a chainlike vapor and a networklike liquid. Finite-size effects preclude the simulation of the coexistence in systems with d/sigma<0.1, but extrapolations of the results to d/sigma-->0 yield estimates of the apparent critical parameters for dipolar hard spheres.