Unsupervised learning has become an essential building block of AI systems. The representations it produces, e.g. in foundation models, are critical to a wide variety of downstream applications. It is therefore important to carefully examine unsupervised models to ensure not only that they produce accurate predictions, but also that these predictions are not "right for the wrong reasons", the so-called Clever Hans (CH) effect. Using specially developed Explainable AI techniques, we show for the first time that CH effects are widespread in unsupervised learning. Our empirical findings are enriched by theoretical insights, which interestingly point to inductive biases in the unsupervised learning machine as a primary source of CH effects. Overall, our work sheds light on unexplored risks associated with practical applications of unsupervised learning and suggests ways to make unsupervised learning more robust.