Using the CLEO II detector at the Cornell Electron Storage Ring, we have searched for flavor changing neutral currents and lepton family number violations in D^0 meson decays. The upper limits on the branching fractions for D^0→ℓ^+ℓ^- and D^0→X^0ℓ^+ℓ^- are in the range 10^(-5) to 10^(-4), where X^0 can be a π^0, K_s^0, η, ρ^0, ω, K̅^(*0), or φ meson, and the ℓ^+ℓ^- pair can be e^+e^-, μ^+μ^-, or e^±μ^∓. Although these limits are above the theoretical predictions, most are new or an order of magnitude lower than previous limits
