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The order and arrangement of dimensions (variates) is crucial for the effectiveness of a large number of visualization techniques such as parallel coordinates, scatterplots, recursive pattern, and many others. In this paper, we describe a systematic approach to arrange the dimensions according to their similarity. The basic idea is to rearrange the data dimensions such that dimensions showing a similar behavior are positioned next to each other. For the similarity clustering of dimensions we need to define similarity measures which determine the partial or global similarity of dimensions. We then consider the problem of finding an optimal one- or two-dimensional arrangement of the dimensions based on their similarity. Theoretical considerations show that both, the one- and the two-dimensional arrangement problem are surprisingly hard problems, i.e. they are NP-complete. Our solution of the problem is therefore based on heuristic algorithms. An empirical evaluation using a number of different visualization techniques shows the high impact of our similarity clustering of dimensions on the visualization results.