Most applications are due in December and early January. Applications typically require GRE scores, three letters of recommendation, a writing sample (15-25 pages), a personal statement, and a transcript. By far the most important part of an application is the writing sample. You should consult with a faculty member at least four months before the application is due to insure that you submit a superior writing sample.
Information on Graduate Programs in Philosophy
Where Williams Graduates have been admitted
This list is still being put together. A partial list includes Arizona, Berkeley, Brown, Chicago, CUNY, Harvard, Maryland, Michigan, MIT, Northwestern, Notre Dame, NYU, Pittsburgh, Princeton, Rutgers, Stanford, UCSD, University of Pennsylvania, and Yale.