FORTUNE -- Dear Annie: I've been lucky enough to get several job interviews in the past couple of months, and I've noticed something strange about all of them, which is that the hiring managers have posed what I would call trick questions.
Yesterday an interviewer asked me, "If you were an animal, what animal would you be?" I was so surprised that it took me a few minutes to come up with an answer. I said I was like a dog, "loyal to a fault" -- which made sense, since I stayed with my last employer for 17 years, despite having had other offers -- but I couldn't really tell from his reaction if that was a good response or not.
Other questions I have struggled with: The overly general "Tell me about yourself" (where do I start?) and "How long would you stay with our company?" (how do I know that when I don't even work here yet?). What's the deal with these weird questions, and how are people supposed to answer them? --Dumbfounded
Dear Dumbfounded: J.P. Hansen, president of Omaha-based Hansen Executive Search, was once asked the Barbara Walters-esque what-animal-would-you-be question in a job interview. His answer: A jaguar. Why? Hansen explained that "the jaguar is very versatile, able to patiently wait for its prey for hours on end, then pounce with lightning speed and grace. Plus, it's a cool car!" The hiring manager who was quizzing him smiled, reached into her purse, and pulled out her car keys -- with a Jaguar emblem on the key chain. Hansen got the job.
Of course, that kind of serendipity is rare. Usually, job candidates confronted with the what-animal question (or popular variations like what tree, or what color) are, like you, dumbfounded. Don't feel bad: According to Hansen, that's what interviewers expect.
"The job market is so tight right now, with so many candidates available whose backgrounds and qualifications are so similar to one another, that some hiring managers try to find an 'aha!' moment where they can trip you up, or get you to reveal something you didn't plan to say," he says.
Great. Since there is no way to predict what you might be asked, how do you prepare? Hansen, who was an executive at ConAgra Foods (CAG, Fortune 500), Bristol-Myers Squibb (BMY, Fortune 500), and Carnation/Nestle before launching his recruiting firm in 1994, says job seekers need to go into interviews with enough confidence to handle any wacky question that might come up. The only way to get that confidence: Prepare, prepare, prepare.
"The people who are getting hired are those who have really learned the company and the industry inside out. You have to wow the interviewer with your knowledge," Hansen says. "If you can be very specific and detailed about what's going on -- what competitive challenges the company faces, what changes are happening in the industry -- then stumbling for a moment over the what-animal question isn't going to matter."
Talkback: What is the strangest interview question you've ever been asked, and how did you respond? Leave your comments at the bottom of this story.
In his book The Bliss List (Career Bliss Publications, $19.95), Hansen lists 38 tricky interview questions, with suggestions for how to formulate winning answers. In reply to the second question you mention, "Tell me about yourself," first ask a qualifying question: "Are you interested in my work experience, my personal experiences, or both?" Notes Hansen: "Often, they want a mix of both -- work, plus whatever else may have shaped you and influenced your thinking."
Obviously, this covers an awful lot of ground. "It's really smart to practice answering this question before you go in to an interview," Hansen says. "Practice summing up your whole life in a concise way. If you ramble, you'll probably be disqualified." Ouch.
As for the third question that bugs you, "How long would you stay with our company?" cheer up: "This is a 'buy' signal, indicating that the interviewer is thinking of making you an offer," Hansen writes. The best response: "Put the hot potato back in the interviewer's lap" by saying something like, "I would expect to have a great career with this company. I'm always looking to learn, and I define success as being ready when an opportunity arises. How long do you think I'd be challenged here?" With any luck, you'll get a chance to find out for yourself.
Let's suppose you're knowledgeable, enthusiastic, and can describe your unique attributes and skills (and how they match up with the job) in a compelling way. How can you go wrong? A surefire way is by badmouthing a current or former employer, yet Hansen says he is surprised by how many candidates do it. "When interviewers ask about your last job, or your present one, they are really hoping you don't step on a landmine and say something negative," he observes.
Ironically, he has noticed that, the more smoothly the conversation is going, the greater the likelihood that a candidate will blurt out a damaging comment about a tyrannical old boss or a wrongheaded restructuring. "It's possible to 'click' with an interviewer and get too comfortable for your own good," he says. "There is such a thing as too candid. It's often the kiss of death." So, when it comes to describing your former employers, remember that the animal you most want to resemble is a soft, fuzzy bunny.
Talkback: What is the strangest interview question you've ever been asked, and how did you respond? What questions do you like to ask candidates? Tell us on Facebook, below.