Tactile sensing plays an important role in robot grasping and object recognition. In this work, we propose a new descriptor named Spatio-Temporal Hierarchical Matching Pursuit (ST-HMP) that captures properties of a time series of tactile sensor measurements. It is based on the concept of unsupervised hierarchical feature learning realized using sparse coding. The ST-HMP extracts rich spatio-temporal structures from raw tactile data without the need to predefine discriminative data characteristics. We apply it to two different applications: (1) grasp stability assessment and (2) object instance recognition, presenting its universal properties. An extensive evaluation on several synthetic and real datasets collected using the Schunk Dexterous, Schunk Parallel and iCub hands shows that our approach outperforms previously published results by a large margin.