In my experience, it's delis, specifically, that put out the pickles and sometimes other accoutrements such as slaw, pickled carrots or whatnot. I'm also pretty sure that the delis in my past, in other locales, did likewise.
Vixmom, do the the NYC/LI/NJ diners do it, too, for sure? I don't think the New England ones do. But whenever and wherever it's done, it's a tradition I love.