Terahertz (THz) radiation is a powerful tool with widespread applications ranging from imaging, sensing, and broadband communications to spectroscopy and nonlinear control of materials. Future progress in THz technology depends on the development of efficient, structurally simple THz emitters that can be implemented in advanced miniaturized devices. Here, it is shown how the natural electronic anisotropy of layered conducting transition metal oxides enables the generation of intense terahertz radiation via the transverse thermoelectric effect. In thin films grown on off-cut substrates, femtosecond laser pulses generate ultrafast out-of-plane temperature gradients, which in turn launch in-plane thermoelectric currents, thus allowing efficient emission of the resulting THz field out of the film structure. This scheme is demonstrated in experiments on thin films of the layered metals PdCoO₂ and La_1.84Sr_0.16CuO₄, and model calculations that elucidate the influence of the material parameters on the intensity and spectral characteristics of the emitted THz field are presented. Due to its simplicity, the method opens up a promising avenue for the development of highly versatile THz sources and integrable emitter elements.