We have made measurements of decay modes of neutral D mesons into exclusive final states containing photons using data collected with the CLEO detector at the Cornell Electron Storage Ring. We report observation of D0-->K-pi+pi-pi+pi-0 (charge conjugates are implicit), and present new measurements of the branching ratios for D0-->K-pi+pi-0, D0-->KBAR 0-pi+pi-0-pi-, D0-->KBAR 0-pi-0, KBAR *0-eta, and D0-->KBAR 0-omega. Where possible, results are compared with theoretical predictions for two-body D0 decays.