We report the results of a blind search for flavor-changing neutral current (FCNC), lepton-flavor violating, and lepton-number violating decays of D(sup+), D(sub s)(sup+), and D(sup 0) mesons (and their antiparticles) into 2-, 3-, and 4-body states including a lepton pair. Such decays may involve Flavor-Changing Neutral Currents, Leptoquarks, Horizontal Gauge Bosons, or Majorana Neutrinos. No evidence for any of these decays is found. Therefore, we present 90% confidence level branching-fraction upper limits, typically at the 10(sup -4) level. A total of 51 decay channels have been examined; 26 have not been previously reported and 18 are significant improvements over previous results.