Television News Anchor Question:

Always come prepared to discuss both a strength and weakness. "What is your greatest weakness?" is often one of the most dreaded questions of an interview because, quite frankly, we all believe that we cannot really be honest in answering. To address this question, be brief and be comfortable with silence. You should certainly brainstorm examples of weaknesses (yes — there are some good weaknesses for interviews, especially when they’re fairly honest and you can describe how you’re improving).

In other words, whatever you say, don’t say more than you have to, and remember that you don't have to literally share what you believe to be your greatest weakness. Typically this means choosing a single weakness and one that isn’t very serious (e.g. “I can be a little too aggressive in setting goals” or “I can be very impatient when I’m working on a project I really believe in”) and too central to the job description you’re interested in.