In high-dimensional feature spaces traditional clustering algorithms tend to break down in terms of efficiency and quality. Nevertheless, the data sets often contain clusters which are hidden in various subspaces of the original feature space. In this paper, we present a feature selection technique called SURFING (SUbspaces Relevant For clusterING) that finds all subspaces interesting for clustering and sorts them by relevance. The sorting is based on a quality criterion for the interestingness of a subspace using the k-nearest neighbor distances of the objects. As our method is more or less parameterless, it addresses the unsupervised notion of the data mining task "clustering" in a best possible way. A broad evaluation based on synthetic and real-world data sets demonstrates that SURFING is suitable to find all relevant subspaces in high dimensional, sparse data sets and produces better results than comparative methods.