I have recently posted my first ever preprint, an essentially finished draft of my essay, “An Introductory Concept of Evidence for Medicine,” to the Open Science Framework’s native preprint server (OSF Preprints).
I was surprised it took me as long as it did to find OSF Preprints as a hosting option, which I suppose is simply because I didn’t explore the Center for Open Science (COS) and Open Science Framework (OSF) for myself at first. The OSF Preprints server isn’t listed explicitly on the Wikipedia Preprint page, even though a number of OSF-supported dedicated servers are (e.g. AgriXiv, PaleorXiv, PsyArXiv), but it functions as a broad host for works in any field, with a wide variety of content field classifiers and custom tags available. As it is a free service of the non-profit Center for Open Science, it also conforms to requirements from some journals that preprints be hosted on non-profit servers. Being backed by the COS also confers the benefit that the OSF Preprints service has support guaranteed for the foreseeable future, and field-specific OSF-supported servers (such a PsyArXiv) have already experienced strong uptake, so I feel very comfortable using it for preprint hosting despite its youth and low profile.
For whatever it’s worth, the under-development medical preprint server MedArXiv will also (reportedly) be supported by the OSF, once it goes live.
Edit (11/23/2018): It appears MedRXiv (however it will be spelled) will be hosted by Cold Spring Harbor Laboratory, rather than the OSF.