Fortune has a cool little piece on puzzling interview questions.
So you're up for a great job, and after the usual chitchat the interviewer asks you a question from far left field. The phrase "just for fun" is sometimes invoked here, but clearly fun isn't the point. For instance, your interlocutor may say, "Let's suppose you have a gold chain with seven links. You need to hire an assistant and pay him one gold link per day for seven days. Each day the assistant needs to be paid for his services without underpayment or overpayment. What is the fewest number of cuts you can make to the chain for this to work out?" Or the interviewer may brandish a wine bottle, a coin, and a cork, and say, "I'm going to put this coin in this bottle and then stop the opening with the cork. How would you get the coin out without breaking the bottle or pulling the cork?" (Answers are below.)
I don't ask these types of questions, but I do ask other things to try to gauge the candidate's problem solving abilities. I also try to engage the candidate in casual conversation. You never know what may turn up when you do.