Recommender systems recommend objects regardless of potential adverse effects of their overcrowding. We address this shortcoming by introducing crowd-avoiding recommendation where each object can be shared by only a limited number of users or where object utility diminishes with the number of users sharing it. We use real data to show that contrary to expectations, the introduction of these constraints enhances recommendation accuracy and diversity even in systems where overcrowding is not detrimental. The observed accuracy improvements are explained in terms of removing potential bias of the recommendation method. We finally propose a way to model artificial socio-economic systems with crowd avoidance and obtain first analytical results.