We present new time-series CCD photometry, in the B and V bands, for the moderately metal-rich ([Fe/H] ~ -1.3) Galactic globular cluster (GC) M62 (NGC 6266). The present dataset is the largest obtained so far for this cluster, and consists of 168 images per filter, obtained with the Warsaw 1.3m telescope at the Las Campanas Observatory (LCO) and the 1.3m telescope of the Cerro Tololo Inter-American Observatory (CTIO), in two separate runs over the time span of three months. The procedure adopted to detect the variable stars was the optimal image subtraction method (ISIS v2.2), as implemented by Alard. The photometry was performed using both ISIS and DAOPHOT/ALLFRAME. We have identified 245 variable stars in the cluster fields that have been analyzed so far, of which 179 are new discoveries. Of these variables, 133 are fundamental mode RR Lyrae stars (RRab), 76 are first overtone (RRc) pulsators, 4 are type II Cepheids, 25 are long-period variables (LPV), 1 is an eclipsing binary, and 6 are not yet well classified. Such a large number of RR Lyrae stars places M62 among the top two most RR Lyrae-rich (in the sense of total number of RR Lyrae stars present) GCs known in the Galaxy, second only to M3 (NGC 5272) with a total of 230 known RR Lyrae stars. Since this study covers most but not all of the cluster area, it is not unlikely that M62 is in fact the most RR Lyrae-rich GC in the Galaxy. In like vein, we were also able to detect the largest sample of LPVs known in a Galactic GC. We analyze a variety of Oosterhoff type indicators for the cluster, and conclude that M62 is an Oosterhoff type I system. This is in good agreement with the moderately high metallicity of the cluster, in spite of its predominantly blue horizontal branch morphology -- which is more typical of Oosterhoff type II systems. We thus conclude that metallicity plays a key role in defining Oosterhoff type. [abridged]
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