We study the galaxy stellar mass function in different environments in the local Universe, considering both the total mass function and that of individual galaxy morphological types. We compare the mass functions of galaxies with log10M*/M⊙ ≥ 10.25 in the general field and in galaxy groups, binary and single galaxy systems from the Padova-Millennium Galaxy and Group Catalogue at z = 0.04-0.1 with the mass function of galaxy clusters of the WIde-field Nearby Galaxy-Cluster Survey at z = 0.04-0.07. Strikingly, the variations of the mass function with global environment, overall, are small and subtle. The shapes of the mass functions of the general field and clusters are indistinguishable, and only small, statistically insignificant variations are allowed in groups. Only the mass function of our single galaxies, representing the least massive haloes and comprising less than a third of the general field population, is proportionally richer in low-mass galaxies than other environments. The most notable environmental effect is a progressive change in the upper galaxy mass, with very massive galaxies found only in the most massive environments. This environment-dependent mass cut-off is unable to affect the Schechter parameters and the Kolmogorov-Smirnov test, and can only be revealed by an ad hoc analysis. Finally, we show how, in each given environment, the mass function changes with morphological type, and that galaxies of the same morphological type can have different mass functions in different environments.