Trap-assisted recombination caused by localised sub-gap states is one of the most important first-order loss mechanism limiting the power-conversion efficiency of all solar cells. The presence and relevance of trap-assisted recombination in organic photovoltaic devices is still a matter of some considerable ambiguity and debate, hindering the field as it seeks to deliver ever higher efficiencies and ultimately a viable new solar photovoltaic technology. In this work, we show that trap-assisted recombination loss of photocurrent is universally present under operational conditions in a wide variety of organic solar cell materials including the new non-fullerene electron acceptor systems currently breaking all efficiency records. The trap-assisted recombination is found to be induced by states lying 0.35-0.6 eV below the transport edge, acting as deep trap states at light intensities equivalent to 1 sun. Apart from limiting the photocurrent, we show that the associated trap-assisted recombination via these comparatively deep traps is also responsible for ideality factors between 1 and 2, shedding further light on another open and important question as to the fundamental working principles of organic solar cells. Our results also provide insights for avoiding trap-induced losses in related indoor photovoltaic and photodetector applications.