Gallium nitride was grown on sapphire (0001) substrates by radio frequency plasma assisted molecular beam epitaxy. The surface morphology was characterized during growth by reflection high energy electron diffraction, and ex situ by scanning electron microscopy (SEM), atomic force microscopy (AFM) and x-ray diffraction. It is found that surface morphological features are linked to domains of specific wurtzite crystal polarity, (0001)Ga face or (000 (1) over bar)N face, for Ga-rich growth. For growth on ALN buffer layers, we commonly observe films which consist of largely (0001)Ga polarity material, as confirmed by selective etch tests, with a varying coverage of (000 (1) over bar)N-face inversion domains threading along the growth direction. For growth near stoichiometric conditions, the growth rate of the N-face domains is slightly lower than that for the Ga-face matrix, which results in the formation of pits with inversion domains at their centers. For samples grown by first depositing GaN under N-rich conditions, followed by growth under Ga-rich conditions, a different morphology is obtained, exhibiting large hexagonal flat terraces observable by SEM and AFM. The apparent grain size of these films is increased substantially over films grown using a single step approach. The cross sectional SEM images of the two-step films show a network of voids and columns at the interface between the N-rich and the Ga-rich layers, above which micron-scale islands form and coalesce via lateral growth. Lateral growth may result in reduced defect density and improved crystal quality. The asymmetric x-ray peak (11 (2) over bar 4) width is reduced to approximately 280 arcsec in the two-stage GaN films.