We describe a recently discovered magnetoresistance (MR) effect in semiconducting polymer and small molecule sandwich devices. The MR effect reaches up to 10% in a magnetic field of 10mT at room temperature. This MR effect is therefore amongst the largest of any bulk material. We characterize this effect and discuss its dependence on voltage, film thickness, temperature, electrode materials and (unintentional) impurity concentration in three different organic semiconductors. We found that the MR effect is only weakly temperature dependent and does not depend on sign and direction of the applied magnetic field. To the best of our knowledge, the discovered MR effect is not adequately described by any of the mechanisms known to date.