Usually if you are not cross-marketing (i.e. sending the story to two or three publications in the same publishing area) it's OK, but once someone accepts it, then should one of the other places where you submitted it also want the story you are ethically bound to tell them that it has already been accepted by so-and-so. Sometimes a second serial rights won't matter. I've found these days that a lot of places absolutely won't publish your story if it has already been published in print or on-line. Others don't mind that it's a second printing. One way you can get around this, is to rework the story, write it from a new angle or put in a new lead and update info. This freshens it up and with a new title and focus it's a 'new' unpublished story.
PS for my TRAVEL THRU HISTORY I have no objected to previously published work.