Spontaneous and stimulated Raman scattering (SRS) are studied in ZnWO4 crystals with a wolframite structure. The polarised Raman scattering spectra corresponding to all the six independent Raman tensor components are measured. The frequencies of the complete set of vibrational modes are identified. The threshold pump energies for SRS in ZnWO4 and KGd(WO4)2 crystals are measured upon excitation by picosecond 1047-nm pulses of a Nd:YLF laser. The SRS gains for ZnWO4 crystals are determined based on the measured thresholds and spectroscopic parameters of the crystals.