We have studied hydrogen impurities and related structural properties in state-of-the-art wurtzite InN films with polar, nonpolar, and semipolar surface orientations. The effects of thermal annealing and chemical treatment on the incorporation and stability of H are also discussed. The near-surface and bulk hydrogen concentrations in the as-grown films increase when changing the surface orientation from (0001) to (000 (1) over bar) to (1 (1) over bar 01) and to (11 (2) over bar0), which may be associated with a decrease in the grain size and change of the growth mode from 2D to 3D. Thermal annealing at 350 degrees C in N(2) leads to a reduction of H concentrations and the intrinsic levels of bulk H are found to correlate with the structural quality and defects in the annealed films.