Most applications are due on, or around, the first of January (although some are due in mid-December). Applications typically require GRE scores, three recommendations, 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 Princeton, Pittsburgh, Harvard, Michigan, Northwestern, Arizona, MIT, NYU, Rutgers, Chicago, Maryland, Yale, Stanford, Berkeley, and Notre Dame.