The collision strengths for atom-atom collisions at high speeds are calculated in the first Born approximation. We studied four classes of collisions, distinguished depending upon whether each of the collision partners becomes excited or not. The results of numerical calculations of the collision strengths are presented for all neutral atoms with Z<=18. The calculations are based on atomic form factors and incoherent scattering functions found in the literature. The relative contribution of each class of collision processes to the total collision cross section is examined in detail. In general, inelastic processes dominate for low-Z atoms, while elastic scattering is more important for large Z. Other systematics of the collision strengths are comprehensively discussed. The relevant experimental literature has been surveyed and the results of this work for the three collision systems H-He, He-He, and H-Ar are compared with the data for electron-loss processes. Finally, suggestions are made for future work in measurements of atom-atom and ion-atom collision cross sections.