We present state-of-the-art cross section predictions for the production of supersymmetric squarks and gluinos at the upcoming LHC run with a centre-of-mass energy of sqrt{s} = 13 and 14 TeV, and at potential future pp colliders operating at sqrt{s} = 33 and 100 TeV. The results are based on calculations which include the resummation of soft-gluon emission at next-to-leading logarithmic accuracy, matched to next-to-leading order supersymmetric QCD corrections. Furthermore, we provide an estimate of the theoretical uncertainty due to the variation of the renormalisation and factorisation scales and the parton distribution functions.