We present a combined experimental and theoretical study on the rotationally inelastic scattering of OH (X²Π_3/2, J = 3/2, f) radicals with the collision partners He, Ne, Ar, Kr, Xe, and D₂ as a function of the collision energy between ∼70 cm⁻¹ and 400 cm⁻¹. The OH radicals are state selected and velocity tuned prior to the collision using a Stark decelerator, and field-free parity-resolved state-to-state inelastic relative scattering cross sections are measured in a crossed molecular beam configuration. For all OH-rare gas atom systems excellent agreement is obtained with the cross sections predicted by coupled channel scattering calculations based on accurate ab initio potential energy surfaces. This series of experiments complements recent studies on the scattering of OH radicals with Xe [J.J. Gilijamse, S. Hoekstra, S.Y.T. van de Meerakker, G.C. Groenenboom, G. Meijer, Science 313, 1617 (2006)], Ar [L. Scharfenberg, J. Kłos, P.J. Dagdigian, M.H. Alexander, G. Meijer, S.Y.T. van de Meerakker, Phys. Chem. Chem. Phys. 12, 10660 (2010)], He, and D₂ [M. Kirste, L. Scharfenberg, J. Kłos, F. Lique, M.H. Alexander, G. Meijer, S.Y.T. van de Meerakker, Phys. Rev. A 82, 042717 (2010)]. A comparison of the relative scattering cross sections for this set of collision partners reveals interesting trends in the scattering behavior.