We investigate modulation-doped GaAs-AlGaAs quantum wells by photoluminescence spectroscopy. External gates allow us to tune the carrier densities below 1011 cm - 2, where we observe a crossover from an extended two-dimensional electron system to a regime where negatively charged excitons start to appear. By applying an external magnetic field, we can clearly resolve singlet and triplet excitons and neutral excitons. We find that the Zeeman splittings of the singlet and neutral excitons depend characteristically on the applied magnetic and electric fields. While the Zeeman splitting of the singlet exciton at high magnetic fields is always positive, the splitting of the neutral exciton can be tuned from negative to positive values by the external electric field.