The microscopic cause of conductivity in transparent conducting oxides like ZnO, In{2}O{3}, and SnO{2} is generally considered to be a point defect mechanism in the bulk, involving intrinsic lattice defects, extrinsic dopants, or unintentional impurities like hydrogen. We confirm here that the defect theory for O-vacancies can quantitatively account for the rather moderate conductivity and off-stoichiometry observed in bulk In{2}O{3} samples under high-temperature equilibrium conditions. However, nominally undoped thin-films of In{2}O{3} can exhibit surprisingly high conductivities exceeding by 4-5 orders of magnitude that of bulk samples under identical conditions (temperature and O{2} partial pressure). Employing surface calculations and thickness-dependent Hall measurements, we demonstrate that surface donors rather than bulk defects dominate the conductivity of In{2}O{3} thin films.