Many businesses adopted this practice years ago, and the trend applies to the public sector as well. I once participated as part of a panel interviewing candidates for a state investigatory position, and behavioral questions were among the bureaucratically generated questions we had to ask in an identical manner of each applicant.
So, what should the hopeful interviewee do? As always, prepare. Prepare to answer questions about planning and organizing skills, decision making and leadership, taking calculated risks and sometimes failing, and effective communication and working with people from disparate backgrounds.
While you are at it, pay attention to how your answer is formed. The more specific you can be the better; employers are looking for an example of an event that happened to you and not a broad overview of best practices. Focus your attention on the context, your actions, and the results, or if you like the word what: what was going on, what you did, and what came of it.
Keep in mind that some behavioral questions ask for situations where things did not go your way. It is important with these questions about negative situations to end with a positive; there is always a lesson to be learned, and if you find that lesson, even a story of a bad experience can be an example of building character and skill.
For more information, check out the ABAJournal story and follow the link in that article to a 2005 reprint from the NALP bulletin.