Summary The phenotypes of plants can be influenced by the environmental conditions experienced by their parents. However, there is still much uncertainty about how common and how predictable such parental environmental effects really are. We carried out a comprehensive experimental test for parental effects, subjecting plants of multiple Arabidopsis thaliana genotypes to 24 different biotic or abiotic stresses, or combinations thereof, and comparing their offspring phenotypes in a common environment. The majority of environmental stresses caused significant parental effects, with −35% to +38% changes in offspring fitness. The expression of parental effects was strongly genotype‐dependent, and multiple environmental stresses often acted nonadditively when combined. The direction and magnitude of parental effects were unrelated to the direct effects on the parents: Some environmental stresses did not affect the parents but caused substantial effects on offspring, while for others, the situation was reversed. Our study demonstrates that parental environmental effects are common and often strong in A. thaliana, but they are genotype‐dependent, act nonadditively, and are difficult to predict. We should thus be cautious with generalizing from simple studies with single plant genotypes and/or only few individual environmental stresses. A thorough and general understanding of parental effects requires large multifactorial experiments.