I was asked once - "how many gas pumps are in Raleigh?". I asked back "do you mean pumps for the general public, or do we need to include commercial/industrial pumps too?" and "do you actually mean Raleigh proper or the metro Raleigh area? if so, how do we define that? All of the county?"
Next question was "go to the whiteboard and design a house". I took out the marker, started to draw, then turned and asked "who will be living there? Is this a single family or duplex? mobile home? stick built or modular?" and a couple other questions.
I was told I was the first people to ask questions before drawing.
I take the point of the brainteaser-type questions to be "how do you react to issues that come up where you don't know a lot of stuff?". For some positions, this is less important, but if you're a customer-facing position - even in development, you may interact with customers or other business units - how do you react when you get odd-ball "left field"-type questions? Do you keep your cool? Do you just react and say "that's stupid!"? Do you walk out in protest? Do you probe for more detailed information before making a pronouncement?
More than ever, I think 'brainteaser' questions are far more about personality-judging than intellect or even raw "problem solving" ability.