We report the results of a search for flavor-changing neutral current, lepton-flavor violating, and lepton-number violating decays of D +, D s +, and D 0 mesons (and their antiparticles) into modes containing muons and electrons. Using data from Fermilab charm hadroproduction experiment E791, we examine the πℓℓ and Kℓℓ decay modes of D + and D s + and the ℓ +ℓ − decay modes of D 0. No evidence for any of these decays is found. Therefore, we present branching-fraction upper limits at 90% confidence level for the 24 decay modes examined. Eight of these modes have no previously reported limits, and fourteen are reported with significant improvements over previously published results.