When faced with this question, don't ever go on the defensive or offensive either. If you go on the defensive you'll get nervous and might end up spilling your biggest weakness in the stupidest manner. At the same time, if you go on the offensive and try to impress the interviewer that you simply don't have any weakness at all, you could end up convincing him that you actually have more weaknesses than most others.
So, how to get around this million dollar question? Relax, or at least do your best to relax. Try and figure out why the interviewer wants to know your biggest weakness. Some analysts say that this question help interviewers understand the interviewee's ability to assess his own abilities to deliver.
Interviewers work really hard on interviewee psychology and over a period of time, they get used to looking for honesty in the candidates they interview. Every reaction of an interviewee offers some or other indication to the interviewer and these aren't always uniform across different interviewers.
So the smart thing to do is not to act smart with the interviewer but just reveal some weakness that marginally affects your work but isn't anything alarming. For instance, a candidate once said that when his stomach rumbles noisily prior to lunch or after lunch, he would feel embarrassed and lose his concentration for a few minutes.
Another candidate reportedly said that she loses concentration whenever her system slows down and keeps loading at every click or Save command. Why does she lose concentration for something that routinely happens with most systems? Well, she tends to use the time to chat with colleagues and that slows her momentum.
This is an honest admission of a slight behavioral flaw that can be rectified with very little effort. However, honesty also has a threshold and should not be disclosed if it indicates serious implications on performance.