My Microsoft Program Manager (PM) Position Interview
Had a 30 min on campus interview in which they asked me to design a phone for a 6 year old. The way design problems work is that the candidate is supposed to come up with several ideas and then the interviewer would steer the conversation in a particular direction, at which point you start brainstorming again. For example for the "design a phone for a six year old" i started out with reasons of why the kid would want a phone. Then the interviewer picked one and we continued the discussion on to features the phone would have.
For the 2nd round in Redmond, I had 4 interviews, three of which were an hour long and the lunch interview was 90 mins. They will make you feel extremely comfortable and will be very friendly. The interviewers talk to one another between the interviews so make sure to make a good impression on the first one (not that they are completely biased, but im sure it helps).
Be prepared to talk to them about your personal or school projects and how you "solved problems". List your projects on your resume so then they have an idea already and can ask you specific questions. All of my behavioral questions were from my resume - "tell me about the challenges you faced in this project", "tell me what you did in this project", etc
ASK QUESTIONS BEFORE YOU START ANSWERING!! I cannot emphasize this enough. If its a technical question, ask what format the inputs are available in. If its a design question, put yourself in the shoes of the person working on the problem and ask appropriate questions. The interviewer will be vague on purpose, to see if you can ask smart questions and find out details about the project.