There should be an equivalent question for interviewees to ask - how about "what is your company's greatest weakness?" Or "what would be the worst part about working here?"
I think the sorts of questions an interviewee asks is more revealing than any sort of digging you might do with the standard bullshit interview questions.
Three to four months later (and two or so months before graduating - much closer time-line) I sat down with a hiring manager at a big-co and went over such stock questions and their purpose and interviewed for a different position at the same company which required the same skill set and level - and got the position.
I would say my answer to this question is always honest, but I'll never ask the question myself.
My own stock answer is "sometimes I have trouble delegating".
To date no one has every asked me this - and when hiring I've never asked it.