The paper first reports an experimentally identified list of benchmark data sets that are hard for representative classification and feature selection methods. This was done after systematically evaluating a total of 54 combinations of methods, involving nine state-of-the-art classification algorithms and six commonly used feature selection methods, on 129 data sets from the UCI repository (some data sets with known high classification accuracy were excluded). In this paper, a data set for classification is called hard if none of the 54 combinations can achieve an AUC over 0.8 and none of them can achieve an F-Measure value over 0.8; it is called easy otherwise. A total of 17 out of the 129 data sets were found to be hard in that sense. This paper also compares the performance of different methods, and it produces rankings of classification methods, separately on the hard data sets and on the easy data sets. This paper is the first to rank methods separately for hard data sets and for easy data sets. It turns out that the classifier rankings resulting from our experiments are somehow different from those in the literature and hence they offer new insights on method selection.