We have used molecular beam epitaxy (MBE) to deposit gallium (Ga) doped ZnO (ZnO:Ga) films. The as-deposited ZnO:Ga films have worked as ohmic contacts for the p-type GaN layers without any kinds of post annealing process. The as-deposited ZnO:Ga films on a-plane sapphire substrates have resistivities of 2-4×10-4 Ωcm, and over 80 % transparency in the near-UV and visible wavelength regions. The brightness of InGaN light-emitting diodes (LEDs) with ZnO:Ga p-contacts has doubled compared to LEDs with conventional Ni/Au semi-transparent p-contacts when measuring the brightness from right above the device surfaces. In addition, using MBE, we have grown homoepitaxial polar ZnO films on (000+1)-plane (+c-plane) ZnO substrates, and also grown non-polar ZnO films on (1-100)-plane (m-plane) and (11-20)-plane (a-plane) ZnO substrates. Growth temperatures have not affected nitrogen-doping levels for +c-axis oriented (Zn-polar) nitrogen doped ZnO (ZnO:N) films. The phenomena were quite different from that for (000-1)-axis (-c-axis) oriented (oxygen-polar) growth, where nitrogen concentrations in ZnO decrease with increasing growth temperatures. We have observed c-axis direction growth for both of m-axis and a-axis oriented films. Oxygen-rich growth conditions flatten surfaces for both m-axis and a-axis oriented films, and the surfaces of m-axis oriented ZnO films flatten with increasing growth temperatures. Nitrogen concentrations in m-axis oriented ZnO:N films have been independent on growth temperatures.