We demonstrate two-dimensional arrays of Bose-Einstein condensates (BECs) as a new experimental platform with parallel quantum simulation capability. A defect-free array of up to 49 BECs is formed by loading a single BEC with $50 000$ atoms into $7×7$ optical wells. Each BEC is prepared with independent phases, confirmed by matterwave interference. Based on BEC arrays, we realize fast determination of the phase boundary of BECs with attractive interactions. We also observe the stochastic collapse dynamics from the distribution of atom numbers in the array. We show that the collapse of a BEC can occur much faster than the averaged decay of an ensemble. The BEC arrays enable new forms of experiments to drastically increase the measurement throughput and to quantum simulate, say, large 2D Josephson-junction arrays.