We present a detailed study of the structural characteristics of molecular beam epitaxy grown nonpolar InN films with a-and m-plane surface orientations on r-plane sapphire and ͑100͒ ␥-LiAlO 2 , respectively, and semipolar ͑1011͒ InN grown on r-plane sapphire. The on-axis rocking curve ͑RC͒ widths were found to exhibit anisotropic dependence on the azimuth angle with minima at InN ͓0001͔ for the a-plane films, and maxima at InN ͓0001͔ for the m-plane and semipolar films. The different contributions to the RC broadening are analyzed and discussed. The finite size of the crystallites and extended defects are suggested to be the dominant factors determining the RC anisotropy in a-plane InN, while surface roughness and curvature could not play a major role. Furthermore, strategy to reduce the anisotropy and magnitude of the tilt and minimize defect densities in a-plane InN films is suggested. In contrast to the nonpolar films, the semipolar InN was found to contain two domains nucleating on zinc-blende InN͑111͒A and InN͑111͒B faces. These two wurtzite domains develop with different growth rates, which was suggested to be a consequence of their different polarity. Both, a-and m-plane InN films have basal stacking fault densities similar or even lower compared to nonpolar InN grown on free-standing GaN substrates, indicating good prospects of heteroepitaxy on foreign substrates for the growth of InN-based devices.