Recently, it has been shown by several groups that the electrical characteristics of organic thin-film transistors (OTFTs) can be significantly influenced by depositing self-assembled monolayers (SAMs) at the organic semiconductor/dielectric interface. In this work, the effect of such SAMs on the transfer characteristics and especially on the threshold voltage of OTFTs is investigated by means of two-dimensional drift-diffusion simulations. The impact of the SAM is modeled either by a permanent space charge layer that can result from chemical reactions with the active material, or by a dipole layer representing an array of ordered dipolar molecules. It is demonstrated that, in both model cases, the presence of the SAM significantly changes the transfer characteristics. In particular, it gives rise to a modified, effective gate voltage V-eff that results in a rigid shift of the threshold voltage, Delta V-th, relative to a SAM- free OTFT. The achievable amount of threshold voltage shift, however, strongly depends on the actual role of the SAM. While for the investigated device dimensions, an organic SAM acting as a dipole layer can realistically shift the threshold voltage only by a few volts, the changes in the threshold voltage can be more than an order of magnitude larger when the SAM leads to charges at the interface. Based on the analysis of the different cases, a route to experimentally discriminate between SAM-induced space charges and interface dipoles is proposed. The developed model allows for qualitative description of the behavior of organic transistors containing reactive interfacial layers; when incorporating rechargeable carrier trap states and a carrier density-dependent mobility, even a quantitative agreement between theory and recent experiments can be achieved.