The New York Times does not publish answers to its crosswords. However, several bloggers have taken it upon themselves to solve each puzzle and publish online, including Rex Parker and William Ernest Parker
Rex Parker of Rex Parker Does the NYTimes Crossword Puzzle solves each puzzle published in the popular newspaper and writes a small description of some of the problem he ran into and how he solved them.
William Ernest Parker of NYTCrossword.com has early access to each day's puzzle, which he solves the night before, posting the answers before the puzzle is even published. He claims to start freehand, then use Google and Wikipedia to solve the stumpers.