The consideration of galaxies as self-gravitating systems of many collisionless particles allows us to use methods of statistical mechanics for inferring the distribution function of these stellar systems. Actually, the long-range nature of the gravitational force contrasts with the underlying assumptions of Boltzmann statistics, where the interactions among particles are assumed to be short-ranged. A particular generalization of the classical Boltzmann formalism is available within the non-extensive context of Tsallis q-statistics, subject to the non-additivity of the entropies of subsystems. Assuming stationarity and isotropy in the velocity space, when solving the generalized collisionless Boltzmann equation it is possible to derive the galaxy distribution function and density profile. We present a particular set of non-extensive models and we investigate their dynamical and observable properties. As a test of the viability of this generalized context, we fit the rotation curve of M33, showing that the proposed approach leads to dark matter haloes in excellent agreement with the observed data.