Gate-voltage dependence of carrier mobility is measured in high-performance field-effect transistors of rubrene single crystals by simultaneous detection of the longitudinal conductivity sigma(square) and Hall coefficient R(H). The Hall mobility mu(H) (identical with sigma(square)R(H)) reaches nearly 10 cm(2)/V s when relatively low-density carriers (<10(11) cm(-2)) distribute into the crystal. mu(H) rapidly decreases with higher-density carriers as they are essentially confined to the surface and are subjected to randomness of the amorphous gate insulators. The mechanism to realize high carrier mobility in the organic transistor devices involves intrinsic-semiconductor character of the high-purity organic crystals and diffusive bandlike carrier transport in the bulk.