It depends on what exactly you're interviewing for, but the best answers will show that you have the ability to recover and/or learn from your mistakes. The interviewer isn't trying to trick you into talking yourself out of the job (although that is what it feels like), they are hoping to hear an example of your ability to grow or adapt.
"The biggest mistake that was made on my part was when I sent off mailings to an incorrect address. I was new at my job and the industry, and I was easily intimidated. I felt that if I asked questions I would be assumed to be ignorant, so I just guessed and due to that it caused me to make a mistake. Now that I am more experienced and mature, I feel that there is no such thing as an incorrect question and communication is very crucial to avoid mistakes and execute a job to the employer's satisfaction."
"The first job I ever had was at a small privately owned coffee shop. Outside of helping my father with his business and attending school I had no professional experience. I believed that always following the rules rigidly was the proper way to handle things. My big mistake was telling a customer, 'I can't do that,' when I should have responded with, 'Let me see what I can do for you.' I realize now that in a situation involving people who are customers or clients you must approach the situation delicately and in a way that says, 'I am doing everything in my power, I want to help you.'"
YOU
The failure to solve debt.
what was your biggest accomplishment in my career
George Foreman
Humanity?
he died
having a son
he died
bEING ALIVE
Also known as the biggest downfall of the world "berry juice" has to be mankinds biggest failure.
Successful. She probably hasn't ever had a career failure.
The two biggest races that have eluded Tony Stewart in his career have been the Daytona 500 and the Indianapolis 500.