Neutron scattering has been used to reveal the nature of the magnetic ordering of the rare earth ions in 1-2-3, 2-4-8, 2-4-7 and 2-1-4 oxide superconductors. The interactions are found to be antiferromagnetic in nature and quite weak, leading to ordering temperatures which are a few degrees Kelvin or less. In the first three systems the separation of the rare earth ions is much larger along the c axis than along the a-b directions, which renders these materials prototypical two-dimensional (2D) magnets. In the ErBa2Cu3O7 and DyBa2Cu3O7 systems, for example, a rod of scattering characteristic of 2D behavior is readily observed, while the order parameter obeys the exact solution of the S = 1/2, 2D Ising model. An extreme case of 2D behavior is found for the DyBa2Cu4O8 material, where a geometric cancellation of the already weak interactions occurs along the c axis, effectively decoupling the rare earth a-b layers. The system thus exhibits no crossover to the 3D behavior usually found well below the ordering temperature, making it the best example of a 2D magnet known to date.