Scientific studies of society increasingly rely on digital traces produced by various aspects of human activity. In this paper, we use a relatively unexplored source of data, anonymized records of bank card transactions collected in Spain by a big European bank, in order to propose a new classification scheme of cities based on the economic behavior of their residents. First, we study how individual spending behavior is qualitatively and quantitatively affected by various factors such as customer's age, gender, and size of a home city. We show that, similar to other socioeconomic urban quantities, individual spending activity exhibits a statistically significant superlinear scaling with city size. With respect to the general trends, we quantify the distinctive signature of each city in terms of residents' spending behavior, independently from the effects of scale and demographic heterogeneity. Based on the comparison of city signatures, we build a novel classification of cities across Spain in three categories. That classification is, with few exceptions, stable over different ways of city definition and connects with a meaningful socioeconomic interpretation. Furthermore, it appears to be related with the ability of cities to attract foreign visitors, which is a particularly remarkable finding given that the classification was based exclusively on the behavioral patterns of city residents. This highlights the far-reaching applicability of the presented classification approach and its ability to discover patterns that go beyond the quantities directly involved in it.