Argumentation skills are an essential toolkit for large language models (LLMs). These skills are crucial in various use cases, including self-reflection, debating collaboratively for diverse answers, and countering hate speech. In this paper, we create the first benchmark for a standardized evaluation of LLM-based approaches to computational argumentation, encompassing 33 datasets from previous work in unified form. Using the benchmark, we evaluate the generalizability of five LLM families across 46 computational argumentation tasks that cover mining arguments, assessing perspectives, assessing argument quality, reasoning about arguments, and generating arguments. On the benchmark, we conduct an extensive systematic analysis of the contribution of few-shot examples, reasoning steps, model size, and training skills to the performance of LLMs on the computational argumentation tasks in the benchmark.