The Statement of Purpose (also called "Letter of Intent" or "Application Essay" or something like that) is by far one of the most important parts of your application. Often it is the only way the admissions committee can evaluate your writing skills. Many applications will specifically tell you what they want you to address in this essay, but usually the instructions are vague. Here are some tips:
Plan on spending a lot of time on this essay. This will probably be the most difficult 1-2 page essay you've ever written. Most people I know take a month or more to write the essay--writing, rewriting, letting it sit and pondering what's been written, and then returning to it to do more editing, rewriting, tearing-it-up-and-starting-it-over-againing, and writing some more.
Solicit comments from professors and graduate students whom you know well--they can guide you as to what to focus on, what sounds too goofy or cheesy to include, what sounds like immature writing, etc. You can also give it to an english major friend of yours--english, philosophy, and comparative literature majors typically write far better than the average Psychology major and should be able to help you make your language sound smoother.
It is common for students to use the most advanced vocabulary they can muster, but what usually results is some perversion of English worth rolling your eyes at. For example, the very tacky sentence "I endeavor to pursue my doctorate in the field of cognitive psychology because I believe human thought permeates all facets of human behavior--from exam-taking to abhorrent aggression--and I believe that, as a cognitive psychologist, I would find the profession fulfilling to such a degree that I would be ecstatic regarding my chosen profession" would have sounded much better like this: "I want to get my PhD in cognitive psychology because I think it's an intriguing field and I know I'd be happy working in it". Most of us don't write as well as we think we do--so make sure you solicit comments from people whom you know to be better writers than yourself.
Keep it brief. Most applications specify how long the essay should be, but if they don't, stick to 1-2 pages single-spaced. (But double-space it if the instructions tell you to.)
Humor can be dangerous, because most of us aren't very good at making someone laugh whom we've never met before. My advice is to avoid any funny-business unless you're absolutely sure that you can pull it off.
Here is a rough outline you can follow when writing your statement of purpose. But make sure you also follow any instructions on your appliation, and make sure you also follow the advice of your professors.
Your beginning can be original, but don't make it ridiculous. If you don't have a philosophical quote or other profound statement that fits the overall theme of your essay well, just stick to a regular introduction like "I was born in Cleveland, Ohio in 1980...". You absolutely must avoid cheesiness and/or egotism.
Your first paragraph might address any themes you can identify in your life that have pointed you toward your interests in psychology. Maybe you are interested in cultural psychology because your parents moved a lot when you were a kid; maybe you're interested in mental health problems because you had an uncle who was schizophrenic; maybe you're interested in psycholinguistics because you grew up in a bilingual home and you've often thought about how remarkable it is that humans usually succeed at understanding each other; etc. In short, there are probably some themes in your life that parallel your psychological interests. (Caution: talking about your own mental health problems is almost never a good idea.)
After talking very briefly about your upbringing and how it relates to your interest in psychology, spend a few sentences on your college experiences that are relevant to your intended career. Maybe you volunteered in a nursing home, or got a part-time job at a psychiatric hospital (these would only be worth mentioning if you're going into a mental health program). But don't bother going into a lot of detail about these experiences unless they are specifically relevant to your intended career (e.g., don't bother mentioning that you worked in a nursing home if you're applying to a biopsychology program).
Move on to talk about your research experience, and, especially if you're applying to a PhD program, spend most of the time in your essay talking about what you learned from these experiences. (If you're not applying to a research-focused program, emphasize work experience more than research experience.) Mention the kind of responsibilities you had, who you worked for, what you learned through this experience, etc.
Talk about how you think your past research (or work) experience is specifically relevant to the field you are interested in for graduate school.
As you're finishing up talking about your undergraduate years, you may want to take a moment to comment on your GPA or GRE scores, if you feel like they are not as good as you'd like them to be. You can even mention what your GPA might be under certain situations (e.g., "excluding my freshman year grades, my GPA would be a 3.7" or "if I remove the classes I took when I was a chemistry major, my GPA would be a 3.8").
Then talk about your goals in graduate school, and what you hope to learn and gain while you're there. Express confidence in your ability to be successful in graduate school, but be careful not to sound egotistical.
Then move on to talk about why the program you're applying to is a good choice for your career goals (e.g., "Harvard would be an excellent place for me to study social psychology because Professor Dan Gilbert and I share an interest in affective forecasting, and I sense that I would have wonderful research and publication opportunities at Harvard. I also share Professor Karen Ruggiero's interest in perceived discrimination. Finally, I recognize that the social psychology program at Harvard is an internationally respected one, and this makes me all the more interested in studying there so that I can be confident of obtaining a professorship when I've finished my graduate studies").
It would be wise for you to have at least one paragraph that you change for each school (like the example above). If you give the exact same essay to each school you apply to (which most people do), your essay won't sound as individualized, and you won't be able to talk about which professors you'd like to work with. Many schools put a high priority on whether your research interests match those of their faculty, so you should address any shared interests you might have if you can.
Sometimes it's also important to mention what type of work you would like to be doing after you finish graduate school. Again, focus on how the particular program you're applying to will help you prepare for this type of work.
Obviously, proof-read your essay a zillion times and make sure that there is not a single punctuation or grammatical error in it. Also, I state again, have several good writers (including several who are graduate students or professors) look over your essay for you and offer suggestions.
Above all, keep in mind that the tips on this page are very flexible. You should follow the instructions on your application and the advice of your professors.