I guess it depends on what you mean by "publish".
My group has been putting manuscripts that are pretty much ready for submission out on biorXiv for a while now. The journals we tend to target for peer reviewed publication don't mind us putting preprints out, and it can be a useful way to disseminate stuff quickly. As you all know, jumping peer review hurdles is often a slow and somewhat tedious process, particularly if some of the authors feel compelled to try to play impact factor or prestige indicator games (not many of us are in a position where we don't have to care about these things). It's good to have a preprint out while these processes grind on. In my experience, people do look at our preprints for a wide variety of reasons. Junior lab members who are looking for RA or postdoc jobs but don't have many publications out can sometimes use links to preprints to reassure a potential employer that they do know what is involved in putting a manuscript together. It may also offer some partial protection against getting scooped. But in many metrics that people may use to judge the quality of a researcher's output, preprints don't count. Scopus h-index won't include preprints, for example, and most grant funders won't consider a preprint as an output that is equivalent to a peer reviewed paper. Similarly, many Chinese University departments have firm criteria stating how many papers a candidate has to have published in journals of a given "quartile rank" before they can be considered for hire or promotion, and for this kind of purpose too, an arXiv publication will score zero. So I don't see arXiv preprints replacing peer reviewed articles in the very near future. As I see it, in our field arXiv is a kind of limbo where papers hang out while their authors take the harrowing journey through peer review purgatory so that the papers can finally be admitted to peer reviewed heaven. But while the papers hang in there, they can be useful in a variety of ways, and uploading a manuscript that's about ready to be submitted for peer review to an arXiv server is pretty straight forward. As "publications" in the sense of units of output that are commonly used by the powers that be to quantify a researcher's productivity, arXiv manuscripts are, for the time being at least, essentially worthless, but as "publications" in the sense that they can help you communicate your science in a quick and hassle free manner that is easily publically accessible, they are great .
Best,
Jan
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Prof Jan Schnupp
City University of Hong Kong
Dept. of Neuroscience