I can't tell you about other companies, but ours is pretty straightforward: you tell us what your strongest areas are, we'll give you interviews that line up with those areas. There's no strict guarantees and you should expect a spread of different questions, but whatever it is that you're good at, expect us to offer you a chance to show us that you're good at it.
It's probably only a useful technique at companies which are big enough and flexible enough to find a use for you, whatever your skill set happens to be. For a company that only has one job opening and needs a specific sort of person to fill it, this sort of pick-your-interview-subject approach doesn't help them.
(Trick questions are useless: they primarily serve to make the interviewer feel clever, not to demonstrate the abilities of the candidate)