By means of hybrid functional calculations we investigate the role of native point defects in the electronic properties of InN. We find that nitrogen vacancies are the most energetically favorable defects and act as shallow donors for Fermi-level positions within the band gap. However, their formation energies are too high in order to explain the observed unintentional n-type conductivity in as-grown or annealed InN films. A transition from donor to acceptor behavior occurs at 1.9 eV above the valence-band maximum (VBM), indicating that if nitrogen vacancies are intentionally introduced to increase the carrier concentration, e.g., by irradiating the InN crystals, the Fermi level will saturate at 1.3 eV above the conduction-band minimum (CBM). The other donor defects, i.e., the nitrogen split interstitial, nitrogen antisite, and indium antisite, have even higher formation energies, and thus are also unlikely sources of unintentional n-type conductivity. The indium vacancies and nitrogen interstitials occupying the octahedral sites are deep acceptors with transition levels resonant in the conduction band. These defects exhibit very high formation energies even for Fermi levels well above the CBM. Our results indicate that InN can support very high electron concentrations before compensation by native acceptor defects takes place.