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Beware - this is an eliminator question, designed to shorten the candidate list. Any admission of a weakness or fault will earn you an “A” for honesty, but an “F” for the interview.
PASSABLE ANSWER: Disguise a strength as a weakness.
Example: “I sometimes push my people too hard. I like to work with a sense of urgency and everyone is not always on the same wavelength.”
Drawback: This strategy is better than admitting a flaw, but it's so widely used, it is transparent to any experienced interviewer.
BEST ANSWER: (and another reason it's so important to get a thorough description of your interviewer's needs before you answer questions): Assure the interviewer that you can think of nothing that would stand in the way of your performing in this position with excellence. Then, quickly review you strongest qualifications.
Example: “Nobody's perfect, but based on what you've told me about this position, I believe I' d make an outstanding match. I know that when I hire people, I look for two things most of all. Do they have the qualifications to do the job well, and the motivation to do it well? Everything in my background shows I have both the qualifications and a strong desire to achieve excellence in whatever I take on. So I can say in all honesty that I see nothing that would cause you even a small concern about my ability or my strong desire to perform this job with excellence.”
Alternate strategy (if you don't yet know enough about the position to talk about such a perfect fit):
Instead of confessing a weakness, describe what you like most and like least, making sure that what you like most matches up with the most important qualification for success in the position, and what you like least is not essential.
Example: Let's say you're applying for a teaching position. “If given a choice, I like to spend as much time as possible in front of my prospects selling, as opposed to shuffling paperwork back at the office. Of course, I long ago learned the importance of filing paperwork properly, and I do it conscientiously. But what I really love to do is sell (if your interviewer were a sales manager, this should be music to his ears.)
