The most obvious major that requires college students to take chem courses is a chemistry major. According to the University of Wisconsin-La Crosse's Department of Chemistry and Biochemistry, a chemistry major can ready post-secondary students to begin a career in education or public service as well as gain an academic base for further studies in graduate or professional school. If you have a strong interest in chemistry, you might have a few different major options within the field beyond the basics -- biochemistry or organic chemistry, for example.
Several pre-professional types of programs require students to take chemistry courses. Dentistry, medicine and veterinary programs all have chemistry pre-requisites for admission to graduate school. That said, pre-professional programs in these and similar areas often require chemistry classes. For example, the University of Massachusetts at Dartmouth requires all pre-med majors to take both inorganic and organic chemistry classes. Likewise, the University of Tennessee's pre-veterinary medicine program also includes both types -- inorganic and organic -- of chemistry.
If you are considering a career in nursing, pharmacology or another similar health care profession, it's likely that you will need to take chemistry courses as part of your major. Specific chemistry classes may include intro levels courses, labs, organic chem, biochemistry or specific classes for health care providers. For example, the University of Pittsburgh's School of Nursing's undergraduate nursing program requires freshman to take chemistry for health professions. Other health-related majors, such as Armstrong Atlantic State University's bachelor of science in respiratory therapy, require science courses such as chemistry to graduate.
College students who have an interest going into the education field may need to take chemistry, depending on what grade level and subject they wish to teach. While it's not likely that your school will require you to take chemistry classes or labs to graduate with a degree in early childhood education, you may need to for a secondary certification track. For example, the bachelor's of middle level education at Duquesne University requires students to complete at least 12 credits in science. Additionally, specialized programs that train teachers to become science teachers -- such as a high school lab instructor -- necessitate college-level chemistry classes.