Here is my collection of prompts for writing a statement of purpose.

Rutgers

In general, your personal statement should be approximately 500 1000 words (2-4) pages and should speak to your qualities and experiences as a student, future researcher, and should clarify how the program and degree you are applying for will be important to the achievement of your goals. Discuss courses taken that have a particular relevance to the program or work experiences that pertain to your career ambitions.

Michigan

The Statement of Purpose should be a concise, well-written essay about your mathematical background, your career goals, and how Michigan's graduate program will help you meet your career and educational objectives.

Caltech

Provide a brief statement of your scientific and professional interests and objectives. Include a description of your past accomplishments that are not evident from the examination of the other documents submitted. Report, if applicable, on any research in progress. List any membership in scientific, professional, or honorary societies. The applicant must write the statement in English. It must not be written in another language and translated for the applicant by another person.

Wisconsin

What are your reasons for graduate study? Please describe your current degree goals and your reasons for selecting a field of study.

San Diego

1. How did you become interested in this field? Establish that you have had a long-term interest in the field and that you have taken positive steps in pursuing your interest. Give the committee members a sense of your particular talents and abilities and their relevance to your academic interests.
2. What experiences have contributed toward your preparation for further study in this field? Demonstrate your interest by providing examples of research experiences, internships, work experience, community service, publications, or life experiences. Briefly describe what you did in each experience. Also, make sure to articulate what you have learned about the field and how those lessons stimulated you to pursue an advanced degree.
3. What are your future goals? Specifically state your degree objective (Master's or Ph.D.) and specify what subdisciplines you are interested in pursuing. For example, if you are applying in political science, the committee needs to know whether you are pursuing American Politics, Comparative Politics, International Relations, or Political Theory. Let the reader know that you are planning a future career as a university professor, researcher, or consultant, or in public service or private practice (or whatever your goal happens to be).
4. What are your research interests? Within your subdiscipline, you should be able to identify one or two topics that are of interest to you. When possible, be specific about your research agenda. Remember that you will be working with professors in research; therefore, your research interests should parallel those of the faculty. (You will usually not be expected to know exactly what you want to research; faculty know that initial interests often change.)
5. How are you a "match" for the program to which you are applying? Explain what attracts you most to the institution/program to which you are applying. Align your research interests with those of one or more of the affiliated professors. The better the "match" with the program/professors, the better the chance that you will be admitted.

Other factors to weave in (remember these are secondary factors):
* Give examples of personal attributes or qualities that would help you complete graduate study successfully.
* Describe your determination to achieve your goals, your initiative and ability to develop ideas, and your ability to work independently.
* Describe background characteristics that may have placed you at an educational disadvantage (English language learner, family economic history, lack of educational opportunity, disability, etc.).
* Leave the reader believing that you are prepared for advanced academic work and will be successful in graduate school.

Berkeley

Please describe your aptitude and motivation for graduate study in your area of specialization, including your preparation for this field of study, your academic plans or research interests in your chosen area of study, and your future career goals. Please be specific about why UC Berkeley would be a good intellectual fit for you.