We report a comparative neutron scattering study of the molecular mobility and nonexponential relaxation of three structurally similar glass-forming liquids, isopropanol, propylene glycol, and glycerol, both in bulk and confined in porous Vycor glass. Confinement reduces molecular mobility in all three liquids, and suppresses crystallization in isopropanol. High-resolution quasielastic neutron scattering spectra were fit to Fourier transformed Kohlrausch functions exp[-(t∕τ)(β)], describing the α-relaxation processes in these liquids. The stretching parameter β is roughly constant with wavevector Q and over the temperature range explored in bulk glycerol and propylene glycol, but varies both with Q and temperature in confinement. Average relaxation times <τ(Q)> are longer at lower temperatures and in confinement. They obey a power law <τ(Q)> ∝ Q(-γ), where the exponent γ is modified by confinement. Comparison of the bulk and confined liquids lends support to the idea that structural and∕or dynamical heterogeneity underlies the nonexponential relaxation of glass formers, as widely hypothesized in the literature.