The charge transport in high quality single crystals of various organic molecular semiconductors is investigated. Band-like motion in delocalized states is observed in various polyacene and oligothiophene single crystals. The electric field dependence of the mobility is ascribed to acoustic phonon scattering. Furthermore, hot carrier effects can be observed at low temperatures and high electric fields. Band-like transport changes over to hopping motion when the effective bandwidth shrinks, i.e. at high temperatures or in crystallographic directions of small molecular orbital overlap.