When your poem or story is published, you grant certain rights for that particular piece to that particular publication. Generally, newspapers, magazines, and literary journals want first serial rights, which give them the rights to publish the story or poem for the first time in a periodical. (These are also called serials, hence “first serial rights.”) Once that happens, the first serial rights have been used for that particular piece and you no longer have them to sell (or give). Why this desire for first serial rights? Most journals want to publish new creative work, and being the first to publish a piece allows that. Also, editors may feel that a previously published work has already made the most of its market, so there’s no need to publish it again.
Usually rights revert back to you after the work is published and, at that point, you can have it published elsewhere. Very few periodically are willing to reprint a story or poem that has been published elsewhere, but those that do state it clearly in their writers’ guidelines. If an editor has her eye on a specific piece she wants to reprint, she’ll seek out the author herself, but this usually only happens with very well known writers. And even then, it’s not too common. More often, writers will republish the poem or story in an anthology or a collection. If you do this, it is good practice to acknowledge the journal that first published the work.
Since the winning entries for contests are often considered for publication, the same is true for contest entries. Even when publication is not an issue, journals are often looking to honor new work that hasn’t already received attention. As with submissions for publication, if previously published work is accepted, this will be stated in the contest guidelines.
While this is the norm in the industry, individual guidelines and contracts vary. Always make sure you know what the journal or contest is seeking and what they ask for in return. Read contracts thoroughly. Some journals ask for more rights or give other stipulations for future publications of the material. It’s important for you to know exactly what you’re agreeing to.