We present multi-colour time-series CCD photometry of the solar-age galactic open cluster M67 (NGC 2682). About 3600 frames spread over 28 nights were obtained with the 1.5 m Russian-Turkish and 1.2 m Mercator telescopes. High-precision observations of the close binary stars AH Cnc, EV Cnc, ES Cnc, the delta Scuti type systems EX Cnc and EW Cnc, and some long-period variables belonging to M67 are presented. Three full multi-colour light curves of the overcontact binary AH Cnc were obtained during three observing seasons. Likewise we gathered three light curves of EV Cnc, an EB-type binary, and two light curves of ES Cnc, a blue straggler binary. Parts of the light change of long-term variables S1024, S1040, S1045, S1063, S1242, and S1264 are obtained. Period variation analysis of AH Cnc, EV Cnc, and ES Cnc were done using all times of mid-eclipse available in the literature and those obtained in this study. In addition, we analyzed multi-colour light curves of the close binaries and also determined new frequencies for the delta Scuti systems. The physical parameters of the close binary stars were determined with simultaneous solutions of multi-colour light and radial velocity curves. Finally we determined the distance of M67 as 857(33) pc via binary star parameters, which is consistent with an independent method from earlier studies.