We perform a comprehensive study of a number of rare charm decays, incorporating the first evaluation of the QCD corrections to the short distance contributions, as well as examining the long range effects. For processes mediated by the c⃗ul+l- transitions, we show that sensitivity to short distance physics exists in kinematic regions away from the vector meson resonances that dominate the total rate. In particular, we find that D⃗πl+l- and D⃗ρl+l- are sensitive to nonuniversal soft-breaking effects in the minimal supersymmetric standard model with R-parity conservation. We separately study the sensitivity of these modes to R-parity violating effects and derive new bounds on R-parity violating couplings. We also obtain predictions for these decays within extensions of the standard model, including extensions of the Higgs, gauge and fermion sectors, as well as models of dynamical electroweak symmetry breaking.