One of the worst answers you can give is an answer that sounds phony. When I was in college, I was desperate for a job as I have a liberal arts BA. I carelessly applied and interviewed for a Data Entry Clerk position for a non-profit organization that deals with family/children social work. Please note that this job probably paid shit and wasn't anything worthwhile. I considered it practice as this was my first ever real job interview and it clearly showed in my interview.
When they asked me what my greatest weakness was, I replied:
"My greatest weakness is I focus too much on small details. I often become focused at the task at hand which leads me to lose sight of the greater picture."
This pretty much says nothing about me and sounded like a rehearsed answer that I scripted. It's really a non-answer and I could tell my interviewers were frustrated with it because they knew it was bullshit.
The best way to answer the weakness question is to give a legitimate weakness, but phrase it in a way that makes it sound not that bad and follow up by suggesting what you have done to work on adjusting that weakness. For example:
"I would say my greatest weakness was my lack of experience using Microsoft Excel when I was in college. I didn't get much exposure to it because I took classes that didn't utilize it. However, when I became interested in working in the XYZ industry, I realized Excel was going to be an important feature so I became proactive and started teaching myself through tutorials and by doing practice assignments. I'm definitely more comfortable in dealing with pivot tables, vlooksup, index/match and if functions now."
Regarding the above, I didn't get the job I mentioned I interviewed for. But it probably wasn't because of the weakness question. It was really just because I didn't give a fuck. Here are some questions I asked when they gave me time for questions. If you are interviewing for a job, here are some questions NOT to ask, courtesy of 21 year old me:
1) So what's the salary for this position? (if the interviewer, usually a HR rep, asks you how much you are looking for, then you can state it, but don't bring it up if you haven't asked)
2) What exactly does your company do? I mean I kinda get an idea of what field its in, but I'm not sure exactly what you guys do. (Yeah, do your research. Don't be like me where I truly dgaf)