We perform a computational screening for two-dimensional (2D) magnetic materials based on experimental bulk compounds present in the Inorganic Crystal Structure Database and Crystallography Open Database. A recently proposed geometric descriptor is used to extract materials that are exfoliable into 2D derivatives and we find 85 ferromagnetic and 61 antiferromagnetic materials for which we obtain magnetic exchange and anisotropy parameters using density functional theory. For the easy-axis ferromagnetic insulators we calculate the Curie temperature based on a fit to classical Monte Carlo simulations of anisotropic Heisenberg models. We find good agreement with the experimentally reported Curie temperatures of known 2D ferromagnets and identify 10 potentially exfoliable 2D ferromagnets that have not been reported previously. In addition, we find 18 easy-axis antiferromagnetic insulators with several compounds exhibiting very strong exchange coupling and magnetic anisotropy.