The stimulated Raman scattering process in a BaWO4 crystal was employed to frequency downshift the first, second, and third harmonics of a Nd:YAG actively-passively mode-locked laser system. Single-pass, double-pass, and external cavity configurations were investigated for this purpose. In each experimental arrangement, the Stokes radiation properties were characterized regarding energy, beam profile, spectrum, and temporal development. The peak pump-to-first-Stokes conversion efficiency was measured to be 55% in the near infrared and 85% in the visible spectral region. The BaWO4 picosecond Raman gain at a pump wavelength of 355 nm was measured to be 38 cm/GW, and a 15% conversion efficiency was achieved. A study of the Raman-cavity output beam profile development as a function of pumping energy was conducted. This work shows that the BaWO4 crystal can be used in picosecond solid-state laser systems as an efficient frequency converter with a wide range of pump radiation wavelengths.