We report first-principles study of the orbital magnetism and magnetic anisotropy energy (MAE) in ultrathin films of Fe, Co, and FePt disturbed from the ferromagnetic ground state. The deviation of ferromagnetic spin configurations from the easy axis leads to the noncollinearity of the spin and orbital moments. In Fe and Co, this noncollinearity correlates with the magnitude of MAE. In contrast, in FePt a complex interplay of competing processes leads to unusual phenomenon of the orthogonality of the inducing spin and induced orbital moments. Considering the influence of noncollinearity of spin moments we obtain opposite trends in the MAE variation for Fe and Co films. This finding correlates with the absence of universal temperature behavior of MAE in itinerant magnets and is shown to originate in the variation of the electronic structure with the change of spin configuration.