Cabibbo-suppressed and Rare Semileptonic $D^0$ and $D^+$ Decays

Using data collected at the $\psi(3770)$ resonance with the CLEO-c detector at the Cornell Electron Storage Ring, we present results of a study of semileptonic decays of the $D$ mesons, including $D^0 \to \rho^- e^+ \nu_e$, $D^+ \to \rho^0 e^+ \nu_e$, $D^+ \to \omega e^+ \nu_e$, $D^+ \to \eta e^+ \nu_e$, $D^+ \to \eta^\prime e^+ \nu_e$, and searches for $D^+ \to \phi e^+ \nu_e$.