The dipole moments of the leptons and quarks are matrices in flavor space, which can potentially reveal as much about the flavor structure of the theory as do the mass matrices. The off-diagonal elements of the dipole matrices lead to flavor-changing decays such as ��-> e ��, while the imaginary parts of the diagonal elements give rise to electric dipole moments. We analyze the scaling of the leptonic dipole moments with the lepton masses in theories beyond the standard model. While in many models the dipole moments scale roughly as lepton mass, it is shown that simple models exist in which the dipoles scale as the cube of the mass or in other ways. An explicit example with cubic scaling is presented, which is motivated on independent grounds from large angle neutrino oscillation data. Our results have great significance for the observability of the electric dipole moments of e, ��and ��, and the rare decays ��-> e ��, and ��-> ����and will be tested in several forthcoming experiments.

19 pages with 5 figures