The amount of oxygen incorporated into MgB2 thin films upon exposure to atmospheric gasses is found to depend strongly on the materials stoichiometry. Rutherford backscattering spectroscopy was used to monitor changes in oxygen incorporation resulting from exposure to: (a) ambient atmosphere, (b) humid atmospheres, (c) anneals in air and (d) anneals in oxygen. The study investigated thin-film samples with compositions that were systematically varied from Mg0.9B2 to Mg1.1B2. A significant surface oxygen contamination was observed in all of these films. The oxygen content in the bulk of the film, on the other hand, increased significantly only in Mg rich films and in films exposed to humid atmospheres.