There is wide-range of programs offered by state universities in USA. Actually, all the courses taught at private universities are also taught at state universities. There is no any course that is specified to be taught at public or private institutions only. So any program you wish to study will be available at a state university of USA. But, not all universities offer all the programs. The number of programs offered may be different on the basis of state university you choose. So make sure to enquire the university about the availability of a program you are interested in.

Mentioning all the programs offered by state universities here isn't possible so I am giving you some links that will take you to list of majors offered at a particular state university.

Ohio State University
http://majors.osu.edu/

Truman State University
http://catalog.truman.edu/content.php?catoid=3&navoid=173

Humboldt State University
http://www.humboldt.edu/~humboldt/programs/type

Montclair State University
http://www.montclair.edu/gradschool/programs/allProgramsA-Z.shtml

Oklahoma State University
http://gradcollege.okstate.edu/degrees/default.php