We present a detailed and uniform study of C, S, Zn and Cu abundances in a large set of planet host stars, as well as in a homogeneous comparison sample of solar-type dwarfs with no known planetary-mass companions. Carbon abundances were derived by EW measurement of two C I optical lines, while spectral syntheses were performed for S, Zn and Cu. We investigated possible differences in the behaviours of the volatiles C, S and Zn and in the refractory Cu in targets with and without known planets in order to check possible anomalies due to the presence of planets. We found that the abundance distributions in stars with exoplanets are the high [Fe/H] extensions of the trends traced by the comparison sample. All volatile elements we studied show [X/Fe] trends decreasing with [Fe/H] in the metallicity range -0.8< [Fe/H] < 0.5, with significantly negative slopes of -0.39±0.04 and -0.35±0.04 for C and S, respectively. A comparison of our abundances with those available in the literature shows good agreement in most cases. Based on observations collected at the La Silla Observatory, ESO (Chile), with the CORALIE spectrograph at the 1.2-m Euler Swiss telescope and with the FEROS spectrograph at the 1.52-m and 2.2-m ESO telescopes, at the Paranal Observatory, ESO (Chile), using the UVES spectrograph at the VLT/UT2 Kueyen telescope, and with the UES and SARG spectrographs at the 4-m William Hershel Telescope (WHT) and at the 3.5-m TNG telescope, respectively, both at La Palma (Canary Islands). Tables 4-16 are only available in electronic form at http://www.edpsciences.org