Background: Software libraries and frameworks play an important role in software system development. The appropriate usage of their functionalities/components through their APIs, however, is a challenge for developers. Usually, API documentation, when it exists, is insufficient to assist them in their programming tasks. There are few API documentation writers for the many potential readers, resulting in the lack of explanations and examples concerning different scenarios and perspectives. The interaction of developers on the Web, on the other hand, generates content concerning APIs from different perspectives, which can be used to document APIs, also known as crowd documentation. Methods: In this paper, we present a study regarding the knowledge generated by the crowd on the Stack Overflow question-and-answer website. Our main goal is to understand how the crowd can contribute for API documentation on two programming tasks: how to implement a scenario using an API (how-to-do-it), and how to fix domain-independent bugs in an existing code where there was a misunderstanding regarding the usage of an API (debug-corrective). We classified questions available on Stack Overflow by the main concerns of askers, and we used those classified as how-to-do-it and debug-corrective to analyze the coverage of API elements on the discussions related to such questions. Our cases included the well-known and popular Swing and Android APIs. Results: Our main findings showed that the crowd provides more content for debug-corrective tasks than for how-to-do-it tasks, regardless of the API. Android API elements are more discussed by the crowd compared to Swing. Moreover, we observed that some API elements are frequently mentioned together in discussions, and that there is a strong association between API coverage on Stack Overflow and its usage in real software systems. Conclusions: Crowd documentation may not be a complete substitute for official documentation because of its partial coverage, especially for how-to-do-it tasks. However, it can still significantly enhance the existent documentation, especially for the most commonly used API elements, providing code samples and explanations on a large variety of usage nuances. Finally, taking advantage of the high coverage for debug-corrective tasks, a new kind of debugging assistant may be conceived.