Part I: Should You Apply, and Where?
Part II: Grades and Classes
Part III: Letters of Recommendation
Part IV: Writing Samples
Part V: Statement of Purpose
I've never read a first draft of a statement of purpose (also called a personal statement) that was any good. These things are hard to write, so give yourself plenty of time and seek the feedback of at least two of your letter writers. Plan to rewrite from scratch at least once.
It's hard to know even what a "statement of purpose" is. Your purpose is to go to graduate school, get a Ph.D., and become a professor. Duh! Are you supposed to try to convince the committee that you want to become a professor more than the next guy? That philosophy is written in your genes? That you have some profound vision for the transformation of philosophy or philosophy education?
Some Things Not to Do
Don't let someone in business tell you how to write a statement of purpose. The kind of sales pitch that results will rub professional philosophers the wrong way. Indeed, bad statements of purpose can go wrong in many ways. For example:
Corny: "Ever since I was eight, I've pondered the deep questions of life."
Brown-nosed: "In my opinion, U.C. Riverside is the best philosophy department in the country." (Shh! Don't let out the secret!)
Unrealistic or arrogant: "I plan eventually to teach philosophy at a top ten philosophy department." (Do you already know that you'll be a more eminent philosopher than the people on your admissions committee?)
Self-important: "I will attempt to revive American pragmatism."
Ignorant: "U.C. Riverside suits my interests especially well because of its strengths in the philosophy of artificial intelligence." (No one here works on AI.)
Self-promoting: "I have always been at the top of my classes and active in class discussions."
Obvious (the least of these sins): "I hope to become a philosophy professor and teach philosophy."
A more subtle way in which statements of purpose can go wrong is in endorsing a particular substantive philosophical position. You are probably not far enough in your philosophical education to justifiably feel confident that you know enough about some particular philosophical issue that your mind is immune to change on it. Thus, saying things like "I would like to defend Davidson's view that genuine belief is limited to language-speaking creatures" comes off as a little bit close-minded and if not exactly arrogant at least not as charmingly humble as you might like. Similarly, "I showed in my honors thesis that Davidson's view...". If only, in philosophy, honors theses ever really showed anything! Much better: "My central interests are philosophy of mind and philosophy of language. I am particularly interested in the intersection of the two, for example in Davidson's argument that only language-speaking creatures can have beliefs in the full and proper sense of 'belief'."
Don't tout your accomplishments. Let your letter writers do that. It comes off so much better! (Make sure, in advance, that your letter writers know what your accomplishments are. See my discussion of letters in Part III.)
Don't tell the story of how you came to be interested in philosophy. It's not really relevant.
What To Write
So how do you fill up that awful, blank-looking page? With a cool, professional description of your areas of interest. If you have, say, three main areas of interest, devote one short paragraph to each of them -- a few sentences describing what questions or subareas within that larger area you find particularly intriguing or have already thought and written about. For example:
I took a two-term independent study course with Prof. Hoffman on Descartes' theory of the passions and its connection to freedom of the will. I anticipate that the history of modern philosophy will continue to be a central interest of mine, especially early modern philosophers' conceptions of the mind. For example, how is Hume's theory of the passions similar to and different from Descartes'? What is the relationship between mentality and personhood for Locke, Hume, and other philosophers of the era? To what extent was Malebranche's occasionalism about causation a development of views already implicit in Descartes?
A statement of this sort tells the committee two things. First, it tells them that you are knowledgeable about the areas of philosophy you plan to study -- not every undergraduate knows about Hume's theory of the passions and Malebranche's occasionalism! -- and it does so without risk of sounding arrogant or close-minded by making pronouncements about what philosophical views are right or wrong. And second, it gives the committee a sense of whether you would be a good fit for the department. If no one in the department teaches the history of modern philosophy (unlikely, actually, but if my example were different the issue could more plausibly arise) or if the people who do teach early modern really focus only on moral and political philosophy (possible), you won't seem like a good match. On the other hand, if the department has specialist(s) in your area(s) of interest, being a "good fit" can boost the likelihood of acceptance.
Explaining Weaknesses in Your File
Although hopefully this won't be necessary, a statement of purpose can also be an opportunity to explain weaknesses or oddities in your file -- though letter writers can also do this, often more credibly. For example, if one quarter you did badly because your health was poor, you can mention that fact. If you changed undergraduate institutions (not necessarily a weakness if the second school is the more prestigious), you can briefly explain why. If you don't have a letter from your thesis advisor because he died, you can point that out.
Tailoring to Specific Schools
It's not necessary, but you can tailor your applications to individual schools. I'm not sure I'd recommend changing your stated areas of interest to suit the schools, though I see how that might be strategic. (If you change them too much, however, there might be some discord between your statement of purpose and the letters of recommendation in your file.) If there is some particular reason you find a school attractive, there's no harm in mentioning that in a final paragraph. For example, you might mention 2-3 professors whose work especially interests you. (But if you mischaracterize them or they don't match your areas of stated interest, this can backfire, so be careful.)
Some people mention personal reasons for wanting to be in a particular geographical area (near family, etc.). Although this can be good because it can make it seem more likely that you would accept an offer of admission, I'd avoid it since graduating Ph.D.'s generally need to be flexible about location and it might be perceived as indicating that a career in philosophy is not your first priority.
On the bright side: Most statements of purpose are flawed in one or more of the ways described above. Committees are used to it and generally don't hold it much against the applicant. Though you can shoot yourself in the foot by coming across as particularly arrogant or poetical or uninformed, this is the one part of the application where standards are low. Philosophers are not, as a rule, especially talented at self-presentation! (I include myself.) The main thing committees want to see is a match between (most of) your areas of interest and what they can teach.
For further advice, see this discussion on Leiter Reports -- particularly for a discussion between the difference between U.S. and U.K. statements of purpose.
Part VI: GRE Scores and Other Things