Does publishing gives you an edge when applying for jobs in industry? I’m in the verge of finishing my PhD next year. I already know I don’t want to follow an academic career; still, I’ve come this far and will see it through (well... I have have a salary too...). I’m starting to look for positions in industry and would like to know how much having publications is appreciated by recruiters. Point in case, some data and drafts have been pilling up in my hard-drive during the last couple of years. Being honest, none of them make for a memorable publication or a significant contribution to science, but there is enough material for two or three submissions to specialized journals. Is it worth putting time and effort in finishing these papers if I’m going into industry? Will my CV look better if I add some publications on it? PS: This is in the context of the US and Europe and I’m getting a PhD in a STEM field.
This depends upon your specific position within any given company. Check out Science Careers for discussions about this, but a summary of some examples for publishing and not publishing:


Some position will not require or expect any publications. These can be technical (e.g., run a machine all day or develop new proprietary methods), managerial, or other types such as sales. 
Some positions will want prior publications to show that you can complete research projects but not expect you to publish when you are working them.
Some companies such as environmental consulting firms expect their scientists to publish so that they continue to be experts in their field and highlight their publications on their webpages (e.g., WEST).
Some companies publish with their clients (e.g., look at the author affiliations on this publication).


In summary, publication expectations in industry range from none to regular publications. I suggest you find people doing jobs you are interested in doing, get to know them, and see what their specific expectations are for publishing. The Ask-the-headhunter blog contains suggestions for breaking into new fields as does the previously mentioned Science Career page. Also, the Chronicle of Higher Education has many resource for people seeking "alternative" careers (e.g., here).