Here's a pretty extensive list of ones I've heard in the ATC world:
Tell us about yourself,
Why do you want to be an FLM?
What's an example of a time that you helped defuse a situation,
What is performance management?
Is there a time when you were pressured to compromise your values....and explain that?
What's an example of a time you tried your hardest to meet a deadline, but failed?
How would you help develop an employee's talent?
Describe a time you worked with a difficult employee that caused issues...what did you do, what did you learn from it, what would you do differently?
Describe the IPM process.
What hobbies do you have outside of work?
Tell about a time that you took responsibility for a mistake before anyone knew you made one.
What's a time that you took the lead on a change that wasn't a popular one? What was your approach to it and what was the outcome?
How would you establish a working relationship with your team and natca?
What have you done to prepare yourself for this position?
How do you handle decision made above your level that you don't agree with?
What challenges do you anticipate?
What are your goals in the next 3-5 years?
You're in the tower, and someone says something that may be offensive...how do you handle it?
You have a long time employee, one year from retirement. Performance has barely been adequate and is using sick leave more and more. What's your plan to correct the situation?
Special emphasis on the bolded ones. They'll be the most common.