This dissertation presents an investigation of the properties, especially the electrical properties, of doped ZnO films grown by plasma-assisted molecular beam epitaxy (MBE) under different conditions. The interest in investigating ZnO films is motivated by the potential of ZnO to replace the currently dominant ITO in industries as n-type transparent electrodes and the difficulty in achieving reliable and reproducible p-type ZnO. On the one hand, n-type ZnO heavily doped with Al or Ga (AZO or GZO) is the most promising to replace ITO due to the low cost, abundant material resources, non-toxicity , high conductivity, and high transparency. On the other hand, ZnO doped with a large-size-mismatched element of Sb (SZO) or co-doped with N and Te exhibits the possibility of achieving p-type ZnO. In this dissertation, the effects of MBE growth parameters on the properties of GZO have been investigated in detail. The ratio of oxygen to metal (Zn+Ga) was found to be critical in affecting the structural, electrical, and optical properties of GZO layers as revealed by x-ray diffraction (XRD), transmission electron microscopy (TEM), Hall measurement, photoluminescence (PL), and transmittance measurements. Highly conductive (~2×10-4 Ω-cm) and transparent GZO films (> 90% in the visible spectral range) were achieved by MBE under metal-rich conditions (reactive oxygen to incorporated Zn ratio < 1). The highly conductive and transparent GZO layers grown under optimized conditions were applied as p-side transparent electrodes in InGaN-LEDs, which exhibited many advantages over the traditional thin semi-transparent Ni/Au electrodes. The surface morphologies of GaN templates were demonstrated to be important in affecting the structural and electrical properties of GZO layers. In those highly conductive and transparent GZO layers with high-quality crystalline structures, studies revealed ionized impurity scattering being the dominant mechanism limiting the mobility in the temperature range of 15-330 K, while polar optical phonon scattering being the mechanism responsible for the temperature-dependence for T>150 K. The majority Sb ions were found to reside on Zn sites instead of O sites for lower Sb concentrations (~0.1 at.%), which can lead to a high electron concentration of above 1019 cm-3 along with a high electron mobility of 110 cm2/V-s at room temperature. The reduction in electron concentration and mobility for higher Sb concentrations (~1 at.%) was caused by the deterioration of the crystalline quality. ZnO co-doped with N and Te was also studied and the advantages of the co-doping technique and problems in achieving p-type conductivity are discussed.