The post-Gaussian effective potential (PGEP) of {lambda}{phi}{sup 4} theory is examined in detail for {ital d}=1, 2, and 3 space-time dimensions. The self-energy is computed in the post-Gaussian approximation in order to determine the physical mass and the wave-function renormalization. The four-dimensional, autonomous'' version of the theory (and its O({ital N}) generalization) is also investigated, using dimensional regularization. Serious difficulties are found: one can indeed obtain an autonomous''-like potential, but it becomes unbounded below for a certain range of parameters. Finally, a Yukawa fermion-scalar theory, without scalar self-interactions, is considered. The PGEP for the scalar sector turns out, after renormalization, to be identical to the GEP.