We investigate the interplay of quantum interference effects and electronic-vibrational coupling in electron transport through single-molecule junctions, employing a nonequilibrium Green's function approach. Our findings show that inelastic processes lead, in general, to a quenching of quantum interference effects. This quenching is more pronounced for increasing bias voltages and levels of vibrational excitation. As a result of this vibrationally induced decoherence, vibrational signatures in the transport characteristics of a molecular contact may strongly deviate from a simple Franck-Condon picture. This includes signatures in both the resonant and the non-resonant transport regime. Moreover, it is shown that local cooling by electron-hole pair creation processes can influence the transport characteristics profoundly, giving rise to a significant temperature dependence of the electrical current.

53 pages, 18 figures, revised version (including more data)