I don't like this question - I do a lot of things, answering this question doesn't say a lot about me. It gives a vastly incomplete picture of me. I would say that it is one of those bad generic questions.
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.
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.
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)
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.