We use a Green's tensor method to investigate the spontaneous emission rate of a molecule and the energy-transfer rate between molecules placed in two types of layered geometries: a slab geometry and a planar waveguide. We focus especially on the role played by surface-plasmon polaritons in modifying the spontaneous emission and energy-transfer rates as compared to free space. In the presence of more than one interface, the surface-plasmon polariton modes split into several branches, and each branch can contribute significantly to modifying the electromagnetic properties of atoms and molecules. Enhancements of several orders of magnitude both in the spontaneous emission rate of a molecule and the energy-transfer rate between molecules are obtained and, by tuning the parameters of the geometry, one has the ability to control the range and magnitude of these enhancements. For the energy-transfer rate interference effects between contributions of different plasmon-polariton branches are observed as oscillations in the distance dependence of this rate.