The goal of argumentation mining, an evolving research field in computational linguistics, is to design methods capable of analyzing people's argumentation. In this article, we go beyond the state of the art in several ways. (i) We deal with actual Web data and take up the challenges given by the variety of registers, multiple domains, and unrestricted noisy user-generated Web discourse. (ii) We bridge the gap between normative argumentation theories and argumentation phenomena encountered in actual data by adapting an argumentation model tested in an extensive annotation study. (iii) We create a new gold standard corpus (90k tokens in 340 documents) and experiment with several machine learning methods to identify argument components. We offer the data, source codes, and annotation guidelines to the community under free licenses. Our findings show that argumentation mining in user-generated Web discourse is a feasible but challenging task.