Epitaxial layers of ZnO have been grown on c-plane, (0001) sapphire substrates by plasma assisted molecular beam epitaxy. The oxygen:zinc flux ratio was found to be crucial in obtaining a film with a smooth surface and good crystallinity. When increasing film thickness from ~80 to 220 nm we observed an increase in the streakiness of RHEED images, and XRD revealed a reduction in crystal strain and increase in crystal alignment. A film with surface roughness of 0.5 nm and a XRD rocking curve FWHM of 0.1 for the main ZnO peak (0002) was achieved by depositing a low temperature ZnO buffer layer at 450 °C and then growing for 120 minutes at 700 °C with a Zn-cell temperature of 320 °C and an oxygen partial pressure of 7e-7 Torr. We found novel structures on two samples grown outside of our ideal oxygen:zinc flux ratio. SEM images of a sample believed to have been grown in a Zn-rich environment showed flower like structures up to 150 um in diameter which appear to have formed during growth. Another sample believed to have been deposited in a Zn-deficient environment had rings approximately 1.5 um in diameter scattered on its surface.