This paper contains results on InN growth by Hydride Vapor Phase Epitaxy (HVPE) on various substrates including sapphire, GaN/sapphire, AlGaN/sapphire, and AlN/sapphire templates. The growth processes were carried out at atmospheric pressure in a hot wall reactor in the temperature range from 500 to 650°C. Arrays of nano-crystalline InN rods with various shapes were grown directly on sapphire substrates. Continuous InN layers were grown on GaN/sapphire, AlN/sapphire and AlGaN/sapphire template substrates. X-ray diffraction rocking curves for the (00.2) InN reflection exhibit the full width at half maximum (FWHM) as narrow as 0.075 deg. for the nano-rods and 0.128 deg. for the continuous layers grown on GaN/sapphire templates.