The distributional pattern of words in language forms the basis of linguistic distributional knowledge and contributes to conceptual processing, yet many questions remain regarding its role in cognition. We propose that corpus-based linguistic distributional models can represent a cognitively plausible approach to understanding linguistic distributional knowledge when assumed to represent an essential component of semantics, when trained on corpora representative of human language experience, and when they capture the diverse distributional relations that are useful to cognition. Using an extensive set of cognitive tasks that vary in the complexity of conceptual processing required, we systematically evaluate a wide range of model families, corpora, and parameters, and demonstrate that there is no one-size-fits-all approach for how linguistic distributional knowledge is used across cognition. Rather, linguistic distributional knowledge is a rich source of information about the world that can be accessed flexibly according to the conceptual complexity of the task at hand.