The aim of this study was to determine the impact of different crop production systems (organic, integrated, and conventional) on the yields of several spring wheat (Triticum aestivum L.) cultivars. A field experiment was carried out at the Agricultural Experimental Station of the Institute of Soil Science and Plant Cultivation in Osiny (Poland) in three consecutive growing seasons (2014, 2015, and 2016). Two factors were included in the experiment: the crop production system (organic, integrated, and conventional) and spring wheat cultivars (Kandela, Izera, Ostka Smolicka, and Waluta). The crop production system significantly differentiated the yield, health, and weed infestation of the spring wheat. Wheat yield in the conventional system (6.12 t·ha−1) was higher than in the organic system (3.68 t·ha−1) by 67%, whereas, in the integrated system (7.61 t·ha−1), it was greater than in the organic system by 109%. The lower yields in the organic system were mainly due to fewer ears per m2 and a smaller 1000-grain weight. In the organic system, we also observed a higher infestation of wheat by foliar fungal pathogens and weeds compared with the conventional and integrated systems. The spring wheat cultivars differed in yield structure and resistance to infestation by fungal pathogens. The Waluta and Izera cultivars performed well in all systems but yielded the best in the integrated and conventional ones. The Kandela cultivar was the most suitable for the organic system, as it achieved the highest yield (4.16 t·ha−1). This was mainly due to its ability to form a compact canopy with relatively high ear density, a large 1000-grain weight, and the highest resistance to fungal pathogens. The results for cultivars’ performance in the organic system may be useful for farmers in decreasing yield gaps in relation to integrated and conventional systems.