A large set of high precision full-Stokes spectro-polarimetric observations of the He I D3 line in spicules has been recorded with the ZIMPOL polarimeter at the Gregory-Coudé Telescope in Locarno. The observational technique allows us to obtain measurements free from seeing-induced spurious effects. The instrumental polarization is well under control and taken into account in the data analysis. The observed Stokes profiles are interpreted according to the quantum theory of the Hanle and Zeeman effects with the aim of obtaining information on the magnetic field vector. To this end, we make use of a suitable Stokes inversion technique. The results are presented giving emphasis on a few particularly interesting measurements which show clearly the operation of the Hanle and Zeeman effects in solar chromospheric spicules.