Cross sections for photo-induced bound-free and free-free transitions in plasmas are evaluated in the average-atom approximation and applied to determine opacities of dense plasmas of light elements. Parameters characterizing the plasmas (chemical potential, average ionic charge, free electron density, bound and continuum wave functions, and occupation numbers) are obtained from the average-atom model. Lowest-order calculations of the free-free cross sections, which diverge in the low-frequency limit, are regularized by accounting for the finite electron-ion relaxation time. The resulting analysis provides the basis for average-atom studies of plasma opacities. Such studies are presented for dense lithium, beryllium, boron, and carbon. Applications are given to Rosseland mean opacities of dense hydrogen and deuterium plasmas and to comparisons of free-free to bound-free opacities in shock-compressed plasmas. Average-atom cross section and opacity calculations are extended to plasmas consisting of more than one ionic species, boron nitride, polystyrene, and a composite H, He, C plasma.