Central to the operation of organic electronic and optoelectronic devices is the transport of charge and energy in the organic semiconductor, and to understand the nature and dynamics of charge carriers is at the focus of intense research efforts. As a basic transport property of solids, the Seebeck coefficient S provides deep insight as it is given by the entropy transported by thermally excited charge carriers and involves in the simplest case only electronic contributions where the transported entropy is determined by details of the band structure and scattering events. We have succeeded for the first time to measure the temperature- and carrier-density-dependent thermopower in single crystals and thin films of two prototypical organic semiconductors by a controlled modulation of the chemical potential in a field-effect geometry. Surprisingly, we find the Seebeck coefficient to be well within the range of the electronic contribution in conventional inorganic semiconductors, highlighting the similarity of transport mechanisms in organic and inorganic semiconductors. Charge and entropy transport is best described as band-like transport of quasiparticles that are subjected to scattering, with exponentially distributed in-gap trap states, and without further contributions to S.