What style questions should I ask potential graduate students interviewing for positions in my lab? As a converse to this question, as a professor, I find it difficult to conduct a useful interview. What types of questions should I ask which would give me a good idea as to how (1) productive and (2) self-sustaining of a student the interviewee may be? If different questions are required for each parameter, please mention that in your answer.
I underwent an interview recently from a prospective adviser, and I found the questions he asked of me to be pretty insightful - hence I'm sharing them here.


Why do you want to pursue research in this specific area?

This would highlight the candidate's motivation in wanting to do research in a particular field - and would also tell the professor more about the candidate's exposure to this area.
What made you apply to this lab/university, as a continuation of the previous question?

The answer would tell you whether the applicant had simply browsed the rankings list of universities, or did he/she actually go through the research publications of the lab - and the application was done due to an intersection of the two!
What would you like to be doing post Ph.D.?

There is no "right" answer to this, but it also tells a lot about the candidate's motivation in pursuing a PhD.
Finally, you can ask the candidate to discuss any problem that he is familiar with in that field - doesn't have to be anything fancy/complicated, but that would serve to highlight the clarity of the applicant's reasoning, communication skills, and level of exposure to the field.