The stability of the soil aggregates is an important soil quality indicator, as it affects the soil’s overall functionality. As the soil aggregates are highly affected by agricultural practices, it is essential to know how crops interact with the aggregation process. Therefore, for obtaining more knowledge, this research was conducted in Estonia in an organic crop rotation field experiment from 2012/2013 through 2015/2016 to study the effects of crops (potato → spring barley undersown with red clover → red clover → winter wheat → pea) under different treatments (TC—control; TW—winter cover crops; TW+M—TW with farmyard manure 40 Mg ha−1 per crop rotation). The results showed that in the topsoil (5–10 cm), the soil water-stable aggregate (WSA) content (determined by the wet sieving method) from highest to lowest was following: pea (61.7%), winter wheat (61.6%), spring barley (61.5%), red clover (59.3%), potato (57.1%); whereas in the subsoil (30–35 cm): potato (50.6%), pea (48.5%), red clover (47.9%), spring barley (47.7%), winter wheat (46.4%). Therefore, potato was a noticeable crop, as among the crops, it had the lowest WSA content in the topsoil, while highest in the subsoil. The results shown gave an assumption that the after-effects of some crops (foremost with pea) were noticeable in the soil properties during the following crop. In the topsoil, the differences between crops were significant among crops just for TW and TW+M treatments. In TW, potato was lower than spring barley and winter wheat, but not significantly lower than pea or red clover. In the subsoil, significant differences between crops were observed for TC and TW treatments: in TC, potato was just significantly greater than red clover (but similar to other crops), and in TW, significantly greater than winter wheat. Furthermore, in the topsoil the soil organic carbon (SOC) content was not significantly affected by crops, and the use of winter cover crops generally increased the SOC content while concurrently decreased the WSA content and the soil maximum water holding capacity. This was probably caused by the additional tillage operations which cancelled out the possible benefits for the soil aggregates. As a consequence of the constantly declining SOC content, caused by the weakened soil aggregates, the plant-available P and K contents, especially in the absence of manure applications, decreased as well, probably due to the combination of fixation and removal of plant biomass. Therefore, it is expected that by continuing this trend, the plant growing conditions decline, which in turn will have a negative effect for the aggregate formation and carbon sequestration, which are essential for plant growth.