We propose a novel classification technique whose aim is to select an appropriate representation for each datapoint, in contrast to the usual approach of selecting a representation encompassing the whole dataset. This datum-wise representation is found by using a sparsity inducing empirical risk, which is a relaxation of the standard L0 regularized risk. The classification problem is modeled as a sequential decision process that sequentially chooses, for each datapoint, which features to use before classifying. Datum-Wise Classification extends naturally to multi-class tasks, and we describe a specific case where our inference has equivalent complexity to a traditional linear classifier, while still using a variable number of features. We compare our classifier to classical L1 regularized linear models (L1-SVM and LARS) on a set of common binary and multi-class datasets and show that for an equal average number of features used we can get improved performance using our method.