We present an overview of best practices for publishing data in astronomy and astrophysics journals. These recommendations are intended as a reference for authors to help prepare and publish data in a way that will better represent and support science results, enable better data sharing, improve reproducibility, and enhance the reusability of data. Observance of these guidelines will also help to streamline the extraction, preservation, integration and cross-linking of valuable data from astrophysics literature into major astronomical databases, and consequently facilitate new modes of science discovery that will better exploit the vast quantities of panchromatic and multi-dimensional data associated with the literature. We encourage authors, journal editors, referees, and publishers to implement the best practices reviewed here, as well as related recommendations from international astronomical organizations such as the International Astronomical Union (IAU) and International Virtual Observatory Alliance (IVOA) for publication of nomenclature, data, and metadata. A convenient Checklist of Recommendations for Publishing Data in Literature is included for authors to consult before the submission of the final version of their journal articles and associated data files. We recommend that publishers of journals in astronomy and astrophysics incorporate a link to this document in their Instructions to Authors.