Although it is typically true that philosophy classes will assign papers in lieu of final examinations, and response papers in lieu of problem sets, the range and variety of subjects covered by philosophy is so broad as to allow some classes to be based entirely on problem sets, and others on in-class examinations. Princeton philosophy courses are often cross-listed with other departments (such as PHI/ELE, PHI/PHY, PHI/LIN, PHI/MAT, PHI/POL, PHI/PSY, and many others), making for a diverse set of classes from which to choose. In addition to the regular philosophy option, students can choose between three interdisciplinary tracks in the philosophy department: political philosophy, philosophy of science, or philosophy and linguistics.
The broad nature of philosophy not only makes interdisciplinary study in the major possible, but it also means that a student can pursue almost any certificate of his or her choice. Talk to certificate program administrators and philosophy professors to get an idea of how your course of study will work, but philosophy majors have historically had very little trouble with certificates in conjunction with their work in philosophy.
Junior year independent work consists of participation in a first semester junior seminar followed by a second semester junior paper. Your junior paper allows you great freedom to pursue an area of philosophy that has sparked your interest either directly through classes you have taken, or indirectly through papers you have read, late-night discussions with friends etc. A good junior paper will identify an interesting question, and show excellent understanding of the issues involved in addressing it, including a precise overview of other people's ideas in the area.
Senior year independent work involves a senior thesis that is at minimum 40 pages in length and an oral departmental examination that is 90 minutes on philosophical topics that include the topic of the individual's thesis. This is essentially an extended junior paper, with the caveat that the aim is not only to show an excellent grasp of a topic/question, but also to offer a possible development of current theories and ways to approach the hardest problems raised by these. A good senior thesis will show a grasp of all of the issues involved, and treat each of them coherently and cogently.