We present the first results of a large spectroscopic survey of globular clusters and candidate globular clusters in the nearby M31 galaxy. The survey is aimed at the classification of known candidate M31 clusters and at the study of their kinematic properties. We obtained low-resolution spectroscopy for 133 targets, including 76 yet-to-be-confirmed candidate clusters (i.e. with no previous spectroscopic information), 55 already-confirmed genuine M31 clusters, and 2 uncertain candidates. Our observations allowed a reliable estimate of the target radial velocity, within a typical accuracy of ~+/-20Km/s. The observed candidates have been robustly classified according to their radial velocity and shape parameters that allowed us to confidently discriminate between point sources and extended objects even from low-spatial-resolution imagery. In our set of 76 candidate clusters we found: 42 newly-confirmed bona-fide M31 clusters, 12 background galaxies, 17 foreground Galactic stars, 2 HII regions belonging to M31 and 3 unclassified (possibly M31 clusters or foreground stars) objects. The classification of a few other candidates not included in our survey has been also reassessed on various observational bases. All the sources of radial velocity estimates for M31 known globular clusters available in the literature have been compared and checked, and a homogeneous general list has been obtained for 349 confirmed clusters with radial velocity. Our results suggest that a significant number of genuine clusters (~>100) is still hidden among the plethora of known candidates proposed by various authors. Hence our knowledge of the globular cluster system of the M31 galaxy is still far from complete even in terms of simple membership.