Collisions between galaxy clusters provide a test of the nongravitational forces acting on dark matter. Dark matter's lack of deceleration in the "bullet cluster" collision constrained its self-interaction cross section sigma(DM)/m <1.25 square centimeters per gram (cm(2)/g) [68% confidence limit (CL)] (sigma(DM), self-interaction cross section; m, unit mass of dark matter) for long-ranged forces. Using the Chandra and Hubble Space Telescopes, we have now observed 72 collisions, including both major and minor mergers. Combining these measurements statistically, we detect the existence of dark mass at 7.6 sigma significance. The position of the dark mass has remained closely aligned within 5.8 +/- 8.2 kiloparsecs of associated stars, implying a self-interaction cross section sigma(DM)/m < 0.47 cm(2)/g (95% CL) and disfavoring some proposed extensions to the standard model.