The dissipation below Tc has been studied for representatives of all classes of cuprate high-temperature superconductors, including Ba2YCu3O7-, and Bi and Tl compounds. The results are parametrized in the framework of flux creep, with the largest activation energies found in Ba2YCu3O7. It is argued that the magnitude of dissipative flux motion is more related to the electronic anisotropy of the material than the actual defect structure. The thermally activated flux creep model, whose parameters are extracted from dc measurements, consistently describes also dynamic measurements, including the irreversibility line and the melting transition. Finally, the similarities in dissipative behavior are emphasized between high-Tc materials, very thin films, and layered low-Tc superconductors.