Over the course of your first few couple of years as PhD student, you must read some of the papers that shaped your advisor's mental image of the research landscape---in addition to the papers that your group has published on the relevant topic (in the widest sense). If you decide to work on one of projects your advisor proposes, these readings equip you with the proper background and help you shape your impressions of what is going on. If you decide to bring something new to your advisor's world, you still need to know how to approach him, how to communicate your ideas effectively. The key to effective communication is to know how your advisor thinks and why he thinks so.
I have classified the paper into those categories that are near and dear to my heart. I don't love these papers, some I loathe for their lack of precision, acknowledgment of historical debt, or sloppy writing. Nevertheless, they left an impression, so they have somehow become a part of the group's vocabulary. In addition, learning to distinguish good papers from "must read even though I dislike them" papers may help you develop your own taste.
Note A paper on this list may not be not essential to your dissertation research. It is unlikely to introduce you to modern ways of dealing with my topics of interest. It is unlikely to be fashionable. It is improbable that you will cite it in your dissertation. But, I consider the paper worth your while; reading it is good for your soul.