We present the results of photoluminescence experiments on the negatively charged exciton X- in GaAs/AlxGa1-xAs quantum wells (QW) in high magnetic fields (less than or equal to 50 T). Three different QW widths are used here: 100, 120, and 150 Angstrom. All optically allowed transitions of X- are observed, enabling us to experimentally verify its energy-level diagram. All samples behave consistently with this diagram. We have determined the binding energy E-b of the singlet and triplet state of X- between 23 and 50 T for the 120 and 150 Angstrom QW, while only the triplet E-b is observed for the 100 Angstrom QW. A detailed comparison with recent theoretical calculations shows an agreement for all samples across this entire field range.