We present calculations of the elastic and inelastic conductance through three different hydrocarbon molecules connected to gold electrodes. Our method is based on a combination of the nonequilibrium Green's function method with density functional theory. Vibrational effects in these molecular junctions were previously investigated experimentally by Kushmerick et al. (Nano Leff. 2004, 4, 639). Our results are in good agreement with the measurements and provide insights into (i) which vibrational modes are responsible for inelastic scattering, (ii) the width of the inelastic electron tunneling signals, and (iii) the mechanisms of heating and cooling of the vibrational modes induced by the coupling to the charge carriers.