I disagree - these are the same types of questions you might see on a college application. As far as my experience goes, it's a question that has massive flaws, especially when you deal with people who has an impressive & flexible set of skills/strengths - it selects against some of the very best, since for them, it's difficult to say what is the most significant accomplishment since many accomplishments manifest as significant in different ways. To select one is to likely avoid talk on the others, and to make a snap judgment call on the implicit question of what is significant, which may end up with a flawed answer that the interviewee may not make normally.
That is why I fundamentally disagree with such a question being important for hiring. If you want to test how someone handles pressure, that can be manifested in other ways. If you want someone to discuss their accomplishments, a simple request for the person to describe some of his/her accomplishments would be less flawed (i.e. "Tell me a little about yourself and what you have done") - it would also be less confrontational.
Why would you want to be less confrontational in an interview? The point is to see if the candidate is good or not, not "let's see how I can ask this question in the nicest way possible so I can get a nice and safe response that the candidate will just read off his / her resume".
The fact is this question weeds out people who truly havent' done anything difficult or unable to communicate their achievements properly. If you have an impressive set of skill / strength, then it should be easy enough for you to pick one.
In my mind the question forces the candidate to show the interviewer his / her:
1) Communication skills (i.e, is this person going to tell me all their problems, or just the one major problem that he/she needs help with)
2) What they view as an accomplishment or challenge
3) How they handle challenges
4) Their ambition (i.e, did they take a leadership position in their accomplishment or did they sit back and let everyone lead the project)
And you easily identify communication skills without such a flawed question for the reason I have detailed.
If I were asked this type of question, it would be a huge red flag to me, and potentially a deal breaker due to signaling that the interviewer has not put enough thought into his/her questions. I would be able to answer the question just fine, and it would not reflect poorly on me, but to me, it reflects poorly on the interview process since you are highly unlikely to have a wholesome picture of the candidate when more useful approaches to get more knowledge are pretty clear, and is fraught with the same flaws you see in many typical processes today that are not meant to find optimal candidates.
Could you clarify what your interview process is to get a wholesome picture of a candidate in a 30 minute interview? That would help me understand what your viewpoint is.
Agree that this post has a terrible title and making a hire/no hire on one question is insane, but it's a good question.