We present a general-purpose tagger based on convolutional neural networks (CNN), used for both composing word vectors and encoding context information. The CNN tagger is robust across different tagging tasks: without task-specific tuning of hyper-parameters, it achieves state-of-the-art results in part-of-speech tagging, morphological tagging and supertagging. The CNN tagger is also robust against the out-of-vocabulary problem, it performs well on artificially unnormalized texts.