If there is a complicated or a trap question then this is the one. We know the basis of your selection for a job is your strengths not your weaknesses then why should the interviewer even bother to ask a question like, “What are your greatest weaknesses?” The fact is this too is a question which is asked quite frequently. There is a 50:50 chance you will be asked this question and more often than not it will be lobbed at you in an ever so lighthearted, easygoing manner. If you are not prepared for it you will be hit by this bouncer. Like they say you will not be knocked out by a a hard knock but by the one you did not see coming. Chances are this is the one which will catch you unawares.

This is normally an eliminator question and the purpose it serves is to shorten the list of candidates for the final round of selection. The psychology behind the elimination seems to be why should you even talk about your weaknesses? Why be negative? Some people (usually psychologists) even suggest if you are aware of your weaknesses why have you not worked on them already and got rid of them. So the best strategy to deal with such a question is not to talk about your weaknesses. If you do the interviewer will probably give you credit for honesty but assess you negatively for your being aware of your weakness for sometime and not taking effective steps to improve. Don't even ask me why they do that. I am not a psychologist. All I can tell you is that they do.
One very old, tested and quite acceptable strategy to deal with the question is to disguise one of your strengths as a weakness. Though it has been extensively used by trainers to train candidates for interviews it works most of the time simply because it insures you do not talk about any weaknesses. Of course it occasionally produces hilarious results especially in campus recruitment as sometimes the entire batch of say twenty or even thirty candidates are asked the question and each one invariably talks of the same strength 'disguised as a weakness'. For example they would say something like, "I am so focused and determined to get the job done on time that I drive my people too hard. I am this A type personality and I work with such a sense of urgency that I sometimes forget that not everyone is at the same wavelength."
Interviewers also have fun with this and the moment they realize the batch is prepared with it they twist the question and sometimes ask," OK is your weakness also the fact that you drive them too hard?" The experienced interviewer will obviously know that you will not talk about your weakness and that is how it should be.
The best way to deal with this question in an interview again focuses you on finding out what exactly are your interviewer's needs because you can state them in answer to this question and assure him that you can think of nothing that would stand in the way of your performing the functions that need to be performed in the job you are being interviewed for. Remind them of what they are looking for and show them you have those skills and traits. For example you could say, " Well, I am sure there will be shortcomings in me but based on what I know what qualities are required for this job, I believe, I will be the best choice. I know when you hire people for a job at this level; you are looking for the right qualification and the right kind of motivation to do well. You can see from my records I have both the qualification and a willingness to pursue excellence in whatever I do. So I feel I there should be nothing that could come in the way of my performing well if given the opportunity."
And of course don't end up repeating this passage verbatim. Try and understand what you are doing and convey it in your own language. This will require practice and practice sometimes is boring. Remember, spectacular success is always preceded by a lot of not-so-spectacular practice. If you still do not feel up to it for any reason or you are still not very sure about the qualities the interviewer is specifically looking for, you could confess to a small weakness which is not really a weakness. If you can match it with the requirements of the job so much the better. For example if the position you are being interviewed for is in the PR department, you could say I like people and one of my weaknesses is that I like to party. If it is a teacher's job you are applying for, you could say that one of your weaknesses is that you do not seem to be able to finish off your work in the class room. Students tend to trust you so much that they continue their contact with you even after the class and keep coming to me for advise and guidance. That takes a lot of my time and my family sometimes has a problem with it. Sometimes you could just say with a touch of humor that your biggest weakness is coffee or perhaps chocolates.
The idea is not to focus on weaknesses and be prepared to talk about the interviewer's need and your strengths and how they make a perfect match.