We report results from the second and third seasons of observation with the QUaD experiment. Angular power spectra of the cosmic microwave background are derived for both temperature and polarization at both 100 GHz and 150 GHz, and as cross-frequency spectra. All spectra are subjected to an extensive set of jackknife tests to probe for possible systematic contamination. For the implemented data cuts and processing technique such contamination is undetectable. We analyze the difference map formed between the 100 and 150 GHz bands and find no evidence of foreground contamination in polarization. The spectra are then combined to form a single set of results which are shown to be consistent with the prevailing LCDM model. The sensitivity of the polarization results is considerably better than that of any previous experiment— for the first time multiple acoustic peaks are detected in the E-mode power spectrum at high significance.