Often your best option for getting into a class that is full is to check the enrollment system frequently during the drops and adds period. Some students decide to drop a class after attending the first session, and vigilant students might well be able to add the class on their own. In some instances, if the class is required and the course design can accommodate an extra student, the teaching department might be willing to issue an override to give you access to a closed class. Contact the teaching department to learn what your options are in a specific situation. Certain classes in these areas are open to students who are not majoring in them, although many classes or sections are reserved for majors.
Music has a band, an orchestra, and a glee club open to nonmajors.
Art sometimes has space for nonmajors in introductory classes and in history of art. Theatre allows any student to take certain introductory classes if space is available. Consult a representative of the appropriate department for help in identifying classes that can be taken as electives. Enrollment is on a first come, first serve basis for these popular subjects, so you are more likely to get these classes when you are an upper level student. Class size is restricted according to the teaching design of the class, and overrides are contingent upon a demonstrated need for the class as well as departmental policy.