We present measurements of Collins asymmetries in the inclusive process e+e-→h1h2X, h1h2=KK, Kπ, ππ, at the center-of-mass energy of 10.6 GeV, using a data sample of 468 fb-1 collected by the BABAR experiment at the PEP-II B factory at SLAC National Accelerator Center. Considering hadrons in opposite thrust hemispheres of hadronic events, we observe clear azimuthal asymmetries in the ratio of unlike sign to like sign, and unlike sign to all charged h1h2 pairs, which increase with hadron energies. The Kπ asymmetries are similar to those measured for the ππ pairs, whereas those measured for high-energy KK pairs are, in general, larger.