Uncomfortable and aggressive questions: Even a soft mannered interviewer can put you to test by asking questions like "Why were you fired?"
Aggressive interview behavior: Some hiring managers religiously believe in tough attitude by adopting a show-me attitude when they speak, in their facial expression, body language and behavior. It is your fault to take their attitude or behavior on its face value.
Unexpected interview behaviors: Some interviewers may try to throw you off the ground with unexpected behavior. They may ask you the same question again and again as if they don't get you. You explain several times, each time getting irritated.
Brainteasers: Puzzle questions or teasers have become popular. Anyway, you may not know answers to questions like "How much does the ice in a hockey rink weigh?" But you can explain how it can be found out.
Case interviews: You may be asked to solve a dilemma or you may be given a set of hard choices to select one from them. Case interview tests are meant for testing your knowledge of relevant business issues, quantitative and analytical skills, ability to prioritize and anticipate problems. They are also used to test your communication skills.
How to face such situations
Your response is similar to tactics used in high level salary negotiations:
Know the question and the nature of the answer desired. This can give you time to think. Guess what the interviewer is trying to get at. Don't hesitate to seek clarifications and maybe it is expected of you.
Feel free to express your feelings.
State assumptions, and seek unknown information.
Focus on how you solve the problem.
When you are explaining anything with a story, don't deviate from the main point.
Be honest, direct and open, but refuse to be intimidated.
Aggressive interviewers can smell fear like dogs. Keep in mind that tough interviewers may turn out to be warm hearted.