  The flavor changing neutral current processes $K_L \to \pi^0 e^+ e^-$, $B \to
X_s e^+ e^-$ and $B \to X_s \mu^+ \mu^-$ are studied within the minimal
supersymmetric extension of the Standard Model. We first examine the rates for
these decay modes in the MSSM with a universal soft supersymmetry breaking
sector at a Grand Unification scale. We later relax the universality condition
and investigate the FCNC transitions in a more general class of models with
negligible flavor violation in squark mixing matrices. We find that the MSSM
prediction for the kaon channel's branching fraction differs from its Standard
Model value by at most 30\% over the entire allowed parameter space. On the
other hand, supersymmetric contributions could potentially enhance certain $B
\to X_s \ell^+ \ell^-$ observables by more than 100\% relative to Standard
Model expectations. The impact of supersymmetry upon the $B$ meson modes is
strongly correlated with the MSSM value for the Wilson coefficient of the
magnetic moment operator that mediates $B \to X_s \gamma$.
