The electronic properties of Mg-O divacancy defects at the MgO surface obtained by removing of a pair of O and Mg ions from terrace, step, or corner sites have been investigated using an embedded cluster model. Long-range polarization and lattice relaxation effects have been included through a shell model approach. It is demonstrated that all these defects are electron traps: an addition of one electron to a neutral precursor results in a stable paramagnetic center. We calculate relaxed electron affinities, vertical ionization energies, formation energies, and hyperfine coupling constants of these defects and discuss their relevance for the interpretation of experimental results on the nature of paramagnetic electronic defects at the surface of MgO. These results further extend a concept of surface electron traps beyond simple anion vacancies to more general structural features.