Researchers are producing an unprecedented deluge of data by using new methods and instrumentation. Others may wish to mine these data for new discoveries and innovations. However, research data are not readily available as sharing is common in only a few fields such as astronomy and genomics. Data sharing practices in other fields vary widely. Moreover, research data take many forms, are handled in many ways, using many approaches, and often are difficult to interpret once removed from their initial context. Data sharing is thus a conundrum. Four rationales for sharing data are examined, drawing examples from the sciences, social sciences, and humanities: (1) to reproduce or to verify research, (2) to make results of publicly funded research available to the public, (3) to enable others to ask new questions of extant data, and (4) to advance the state of research and innovation. These rationales differ by the arguments for sharing, by beneficiaries, and by the motivations and incentives of the many stakeholders involved. The challenges are to understand which data might be shared, by whom, with whom, under what conditions, why, and to what effects. Answers will inform data policy and practice.