The field of the globular cluster NGC 3201 was monitored between 1998 and 2009 in a search for variable stars. BV light curves were obtained for 152 periodic or likely periodic variables, fifty-seven of which are new detections. Thirty-seven newly detected variables are proper motion members of the cluster. Among them we found seven detached or semi-detached eclipsing binaries, four contact binaries, and eight SX Phe pulsators. Four of the eclipsing binaries are located in the turnoff region, one on the lower main sequence and the remaining two slightly above the subgiant branch. Two contact systems are blue stragglers, and another two reside in the turnoff region. In the blue straggler region a total of 266 objects were found, of which 140 are proper motion (PM) members of NGC 3201, and another nineteen are field stars. Seventy-eight of the remaining objects for which we do not have PM data are located within the half-light radius from the center of the cluster, and most of them are likely genuine blue stragglers. Four variable objects in our field of view were found to coincide with X-ray sources: three chromospherically active stars and a quasar at a redshift z~~0.5.