This may be a real niche population--medical students who are also poets--but for this group there are two no-cost contests coming up with December 31 deadlines.
First, the William Carlos Williams Poetry Competition, sponsored by the Human Values in Medicine Program of the Northeastern Ohio Universities College of Medicine (NEOUCOM), is open to students attending schools of medicine or osteopathy in the United States and Canada. The contest's final judge is John Stone, M.D., poet and essayist from Emory University School of Medicine. The top three poems will be considered for publication in the Journal of Medical Humanities and will be awarded $300, $200, and $100, respectively. The three winners will also be invited to read their poems at NEOUCOM in April (expenses paid). For more information about this contest (including submission instructions), visit the NEOUCOM website.
And second, "medical undergraduates currently enrolled in accredited U.S. medical schools" may submit poetry for the Baylor College of Medicine's annual Michael E. DeBakey Medical Student Poetry Award. This competition awards the top winner a cash prize of $1,000; the second- and third-prize winner receive $500 and $300, respectively. Note that "All winning poems become the property of the Michael E. DeBakey Medical Student Poetry Award program." The first-prize poem will also be submitted for possible publication in "a major medical periodical." For more information, click here.