I typically ask candidates to implement a function that calculates the nth element of the Fibonacci sequence, write a program that prints the values in a binary tree in ascending order and finally to implement an algorithm that finds the value of the element in the middle of a linked list. These are just "introductory" questions, but very very few candidates make past this stage so I very rarely get to ask serious / deep programming questions to candidates.
And believe me, I'm very forgiving on interviews and try to take into consideration that the candidate is probably very nervous, especially when they are fresh off the school, but what can I do with a candidate who can't figure out how to get the number of elements in a bloody linked list, even after carefully explaining how a linked list works? Or the ones who get the idea that they should be counting all elements but have no idea how? How could I discuss the finer details of type covariance or ask them how they would go on about implementing a face detection algorithm if they can't even come up with the naive solution to the Fibonacci "problem"?