Colleges aim to graduate well-rounded individuals, so they set a minimum standard everyone must meet. Though the exact requirements can vary from college to college, they generally require you to take a few classes in various subjects. For example, the college might say that all graduates must take a certain number of credit hours in the math and sciences, the humanities and the arts. Some schools even have a foreign language and physical education requirement, though you may be able to opt out of these if you can prove language fluency or play a sport.
You might receive a class dean or student adviser for your entire class, along with an adviser in your major area of study. These advisers will help ensure that you meet the requirements set forth in the major. Some areas of study, such as the physical sciences, have a fairly strict progression of classes for majors to take. Others, such as a political science art history major, may have requirements such as taking "four classes at the 300 level," but have flexibility in choosing which specific classes to take.
Ultimately, it's the student who decides which classes she'll take for graduation, as long as these classes fit within the guidelines set by the college and her adviser. For example, an English major might take algebra 101 and astronomy 101 to fulfill the math and science requirement, Japanese classes for a language requirement, and upper-level classes on Shakespeare and young adult fiction to complete her major. A chemistry major, on the other hand, may be required to take chemistry classes from the 100 to 300 level, with fewer choices at the 300 level. She'll then possibly choose to take sociology 101 and political theory classes to fulfill humanities requirements but will have tested out of the language requirement because she grew up speaking German, perhaps.
To a lesser extent, the current job market might play a role in what courses a student takes. For example, if a student is earning a business degree, he might notice that the job listings his senior year are primarily looking for those with experience in marketing, so he'll opt for the upper-level marketing course rather than the upper-level management course. Likewise, a political science major hoping to land a gig overseas might study foreign languages to boost his chances of getting a job after graduation.