The double-{beta}-decay Q values of {sup 130}Te, {sup 128}Te, and {sup 120}Te have been determined from parent-daughter mass differences measured with the Canadian Penning Trap mass spectrometer. The {sup 132}Xe-{sup 129}Xe mass difference, which is precisely known, was also determined to confirm the accuracy of these results. The {sup 130}Te Q value was found to be 2527.01{+-}0.32 keV, which is 3.3 keV lower than the 2003 Atomic Mass Evaluation recommended value and is consistent with another recent Penning trap measurement. The {sup 128}Te and {sup 120}Te Q values were found to be 865.87{+-}1.31 and 1714.81{+-}1.25 keV, respectively. For {sup 120}Te, this reduction in uncertainty of nearly a factor of 8 opens up the possibility of using this isotope for sensitive searches for neutrinoless double-electron capture and electron capture with {beta}{sup +}emission.