I've heard from friends that they ask for the source of your BTC (for a mining friend, he had to take photos of him next to miners, and showcase a lot of other privacy-breaching stuff just to withdraw his funds), as well as other things mentioned by figmentofmyass.
That's bleedin' outrageous. I'd like to know what one's position is if you simply can't supply the info they're demanding. There are tons of dead exchanges and pools with no way of retrieving the information.
That is a question that Bitstamp won't answer...