We have grown epitaxial films of Sr2RuO4, Ba2RuO4, and Sr2TiO4 and studied their structural and transport properties. These phases are all layered perovskites with the K2NiF4 structure. Sr2RuO4 is the only known superconducting layered perovskite that is free of copper (Tc equals 1.35 K in bulk single crystals). In light of the observation that hydrostatic pressure reduces the Tc of Sr2RuO4, we have investigated the effect of replacing Sr2+ with the larger Ba2+ ion. In bulk samples, Ba2RuO4 is not isostructural with Sr2RuO4 when synthesized at atmospheric pressure. However, using pressures of 65,000 atm., the synthesis of a tetragonal form of Ba2RuO4 (with the K2NiF4 structure) has been reported. We have grown epitaxial films of the tetragonal form of Ba2RuO4 through the use of epitaxial stabilization. In addition to studying these ruthenates that are isostructural to the high-Tc superconductor (La,Sr)2CuO4, we have also investigated La-doped Sr2TiO4. Doped SrTiO3 is a well-known superconductor, but the effect of reducing the dimensionality of SrTiO3 from 3-D to 2-D (i.e., Sr2TiO4) has never been reported. The Sr2RuO4 and Ba2RuO4 films have been grown by pulsed laser deposition (PLD); Sr2TiO4 films have been grown by reactive molecular beam epitaxy (MBE). The growth conditions yielding phase-pure films have been mapped out. The orientation of the epitaxial films has been controlled by choosing appropriate substrates. Resistivity versus temperature measurements show that all three materials exhibit metallic conductivity. A resistivity, (rho) varies direct as T2 has been observed in many samples at low temperatures, T. However, superconductivity has not been observed in any samples. In addition to growing Sr2TiO4, the n equals 1 member of the Srn+1TinO3n+1 Ruddlesden-Popper homologous series, we also used the atomic layering capability of MBE to grow phase-pure, epitaxial, thin films of the n equals 2 - 5 members of this homologous series (i.e., Sr3Ti2O7, Sr4Ti3O10, Sr5Ti4O13, and Sr6Ti5O16).