Impulse approximation and pion-exchange current contributions to the trinucleon magnetic moments are calculated using wave functions generated by solving the configuration-space Faddeev equations for a variety of nucleon-nucleon force models. Careful attention is paid to the origin of important exchange current contributions. Numerical results are compared with previously published calculations and with the experimental data. An attempt is made to isolate and understand sources of discrepancy between our results and those previously published. Calculations which include both impulse and pion-exchange current contributions are in fairly good agreement with experiment, whereas calculations which include only the impulse approximation term are not.