Abstract We have derived the global mass functions of a sample of 35 Galactic globular clusters (GCs) by comparing deep Hubble Space Telescope photometry from the globular clusters treasury project (Sarajedini et al. 2007) with suitable multimass dynamical models. For a subset of 29 clusters with available radial velocity information, we were also able to determine dynamical parameters, mass-to-light ratios and the mass fraction of dark remnants. The derived global mass functions are well described by single power laws in the mass range 0.2 < m/ M⊙ < 0.8 with mass function slopes α > −1. Less-evolved clusters show deviations from a single-power law, indicating that the original shape of their mass distribution was not a power law. We find a tight anticorrelation between the present-day mass function slopes and the half-mass relaxation times, which can be understood if clusters started from the same universal initial mass function (IMF) and internal dynamical evolution is the main driver in shaping the present-day mass functions. Alternatively, IMF differences correlated with the present-day half-mass relaxation time are needed to explain the observed correlation. The large range of mass function slopes seen for our clusters implies that most GCs are dynamically highly evolved, a fact that seems difficult to reconcile with standard estimates for the dynamical evolution of clusters. The mass function slopes also correlate with the dark remnant fractions indicating a preferential retention of massive remnants in clusters subject to high mass-loss rates.