Rare and forbidden charm decays are unique probes for hints of physics beyond the Standard Model. The LHCb collaboration has made significant contributions to the field over the last years. This report presents results of the search for the lepton-flavour violating decay $D^0 \rightarrow e^{\pm}\mu^{\mp}$ and the first observations of the rare four body decays $D^0 \rightarrow K^{-} \pi^+ \mu^{+} \mu^{-}$, $D^0 \rightarrow \pi^{+} \pi^- \mu^{+} \mu^{-}$ and $D^0 \rightarrow K^{+} K^- \mu^{+} \mu^{-}$.