North Carolina State University is one of a limited number of land grant universities in the U.S. offering a large program in graduate training for plant breeding. See the survey on student training in plant breeding: http://cuke.hort.ncsu.edu/breeding/pbsurvey/brdsurvey.html
There are openings in graduate school, including full assistantship support, for those students in the biological sciences who have taken the basic science courses. Those courses include calculus, freshman chemistry, organic chemistry, and physics. See requirements at: http://www.cals.ncsu.edu/hort_sci/student/hsgradadmssn.html
Career opportunities for plant breeders with a degree at the M.S. or Ph.D. level include the USDA, land grant universities, seed companies, and international research centers (such as IRRI in the Phillipines) doing research and developing cultivars.
Undergraduate students: talk to your advisor about the courses you are taking for your B.S. degree. Make sure you have the necessary requirements for graduate school. See the web site for Plant Breeding at NCSU: http://www.plantbreedingcenter.ncsu.edu/
If you are interested in a plant breeding career, please see our plant breeding faculty at: https://projects.ncsu.edu/cals/hort_sci/people/faculty/breeding.php