We have conducted a deep (15~<r~<23 ), 20 night survey for transiting planets in the intermediate-age (~550Myr) open cluster M37 (NGC 2099) using the Megacam wide-field mosaic CCD camera on the 6.5m MMT. In this paper we present a catalog and light curves for 1445 variable stars; 1430 (99%) of these are new discoveries. We have discovered 20 new eclipsing binaries and 31 new short-period (P<1day) pulsating stars. The bulk of the variables are most likely rapidly rotating young low-mass stars, including a substantial number (>~500) that are members of the cluster. We identify and analyze five particularly interesting individual variables, including a previously identified variable that we suggest is probably a hybrid gamma Doradus/delta Scuti pulsator, two possible quiescent cataclysmic variables, a detached eclipsing binary (DEB) with at least one gamma Doradus pulsating component (only the second such variable found in an eclipsing binary), and a low-mass (M_P_~M_S~0.6M_{sun}_ DEB that is a possible cluster member. A preliminary determination of the physical parameters for the DEB+gamma Doradus system yields M_P_=1.58+/-0.04M_{sun}_, M_S_=1.58+/-0.04M_{sun}_, R_P_=1.39+/-0.07R_{sun}_, and R_S_=1.38+/-0.07R_{sun}_.