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The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally the Papadopoulos list cite{Papadopoulos1} for Killing-Yano tensors in $G$ structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups $G$ appearing in the Berger classification, and we enlarge the list by considering additional $G$ structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.