The results of an extensive theoretical study of native defects in hexagonal GaN are presented. We have considered cation and anion vacancies, antisites, and interstitials. The computations were carried out using ab initio molecular dynamics in supercells containing 72 atoms. N vacancy introduces a shallow donor level, and may be responsible for the n-type character of as-grown GaN. Due to the wide gap of nitrides, self-compensation effects strongly reduce both n-type and p-type doping efficiencies due to the formation of gallium vacancy and interstitial Ga, respectively.