Magnetic coupling constants (2J) of hydroxo- and alkoxo-bridged copper binuclear compounds have been evaluated to determine the accuracy of different density functional methods and to study the magnetic behavior of these compounds. Comparison between the calculated and experimental coupling constants for the complete structures of five compounds shows that the most successful computational strategy is the combination of the B3LYP method with the broken-symmetry approach. Calculations for model compounds of both families yield reasonable approximations to the values of magnetic coupling constants calculated for the full molecular structures. Our calculations show a correlation between the magnetic coupling constant and the Cu-O-Cu bridging angle and with the out-of-plane displacement of the hydroxo or alkoxo groups, in agreement with the experimental data. The counterions of the hydroxo-bridged complexes, when hydrogen bonded to the bridging hydroxo group, determine the extent of the out-of-plane displacement of its hydrogen atom and strongly influence the sign and magnitude of the magnetic interaction. The energy gap between the two singly occupied molecular orbitals is shown to determine the changes in the value of 2J for small structural variations.