We implement optical spectroscopy to study charged excitons in modulation-doped GaAs/AlGaAs quantum wells. We report the first observation of the positively charged exciton and of the triplet state of the negatively charged exciton. Applying a gate voltage at high magnetic fields, we investigate the transition between metallic and insulating states. We find that while the photoluminescence line of the metallic two-dimensional electron gas transforms smoothly into a negatively charged exciton, the Zeeman splitting of this line exhibits an abrupt change at the metal-insulator transition.