Charge carrier traps are generally highly detrimental for the performance of semiconductor devices. Unlike the situation for inorganic semiconductors, detailed knowledge about the characteristics and causes of traps in organic semiconductors is still very limited. Here, we accurately determine hole and electron trap energies for a wide range of organic semiconductors in thin-film form. We find that electron and hole trap energies follow a similar empirical rule and lie ~0.3-0.4 eV above the highest occupied molecular orbital and below the lowest unoccupied molecular orbital, respectively. Combining experimental and theoretical methods, the origin of the traps is shown to be a dielectric effect of water penetrating nanovoids in the organic semiconductor thin film. We also propose a solvent-annealing method to remove water-related traps from the materials investigated, irrespective of their energy levels. These findings represent a step towards the realization of trap-free organic semiconductor thin films.