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.