Data repositories: when choosing an archival repository, the minimum requirements are that it provide a unique global identifier for your data (typically a digital object identifier, DOI), and that it offer long-term preservation guarantees (at least 10 years). Example repositories satisfying these criteria include: Figshare, Zenodo, DataVerse, and Dryad. It’s important to note that GitHub is not adequate as an archival repository: it provides no guarantee that the artifacts will be preserved, as a project owner can at any time delete a code repository on GitHub.
Digital object identifier, DOI (https://www.doi.org), is a unique string assigned to a digital object by a registration agency, identifying the object and providing a persistent link to it on the Internet. You should deposit your data (and code releases) in a site that assigns a DOI (or an equivalent), and if a DOI is available for an item you cite, you should always include it in the reference list.
Figshare (http://figshare.com/) is a general-purpose repository for all kinds of digital artifacts of research. Any file format can be uploaded, up to 5GB in size. It is free and unlimited for public items, and offers private space limited to 20GB. We use it to deposit presentation slides, research figures, posters, course syllabi, lecture notes, and reproducibility packages to accompany our papers. You retain copyright on all deposited artifacts, and release them under the license of your choice. You can connect your GitHub account and import directly from your repositories there.
Zenodo (https://zenodo.org) is a data repository created by CERN and the European open-access infrastructure project called OpenAIRE. It is free and non-commercial. You can log in with your ORCID, and can deposit large files—up to 50GB by default, but you can request to deposit larger ones. We use it to deposit larger research datasets, and also to archive a full code base from its GitHub repository, to get a DOI for the code at the time of a release or publication. Our lab group has a Zenodo Community, where we collect our joint artifacts: https://zenodo.org/communities/barbagroup/
In comparison with open-source software, open-access publishing has a more tenuous relationship with reproducibility. The Yale Law School Roundtable on Data and Code Sharing \cite{2010} included a recommendation to publish under open-access conditions (or post pre-prints), without making an explicit argument for this inclusion. Our practice is to always post a pre-print on arXiv for our research manuscripts, at the time of submission to a journal (or before). This makes the work available during the sometimes months-long peer-review process. In physics, mathematics, astronomy, and computer science, arXiv is a way of life! We consider having a friendly pre-print policy a basic criterion to choose a journal. Most journals accept manuscripts previously posted to preprint servers, including almost all journals by Elsevier and Nature Publishing Group, most in Springer and Taylor & Francis, and the majority of professional society journals, including 85% in the American Chemical Society (ACS)—chemistry being historically one of the most hard-nosed communities towards preprints, they’ve now founded their own preprint server: ChemRxiv. We’ve seen a semi-explosion of ’Xiv sites in the last few years, with engrXiv, bioRxiv, socArxiv, PeerJ Preprints, Authorea Preprints, and OSF Preprints (from the Open Science Framework). IEEE policy says that "Prior to submission to an IEEE publication: Authors may post their article anywhere at any time, including on preprint servers such as arXiv.org. This does not count as a prior publication."
Besides posting pre-prints, our signature open-science practice is to prepare what we call reproducibility packages, or “repro-packs,” in short. The concept was part of my “Reproducibility PI Manifesto” \citep*{barba2012}. For the main results in a research manuscript, we share a file bundle of data, plotting script & figure under a CC-BY license. We deposit the file bundle as a Figshare object and get a DOI, then cite this DOI in the caption of the same figure in the manuscript. Ostensibly, this was a measure to increase the reproducibility of our results: we also add a “reproducibility statement" in the paper, explaining that the figures, plotting scripts and data were shared just for this purpose. But in conference talks and hallway conversations, I often stressed the fact that this strategy also means that we are asserting the copyright on the figures, releasing them under CC-BY, and reusing them in our own paper under the terms of this license. That leaves the figures open for future reuse by ourselves and others under the license terms, without the need to ask permission from the journal (even if copyright of the paper was transferred to them for publication).