Argument mining is a core technology for automating argument search in large document collections. Despite its usefulness for this task, most current approaches are designed for use only with specific text types and fall short when applied to heterogeneous texts. In this paper, we propose a new sentential annotation scheme that is reliably applicable by crowd workers to arbitrary Web texts. We source annotations for over 25,000 instances covering eight controversial topics. We show that integrating topic information into bidirectional long short-term memory networks outperforms vanilla BiLSTMs by more than 3 percentage points in F1 in two- and three-label cross-topic settings. We also show that these results can be further improved by leveraging additional data for topic relevance using multi-task learning.