I am a very popular choice for thesis committees inside and outside of the department. Unfortunately, I can't be on every committee so I've started interviewing the students to select which committees I do want to be on. Here are some of the questions I ask:
1. Why do you want *me* to be on your committee? (Majority of students are unable to answer this, so maybe I don't need to be on their committee)
2. What are your grades like? (If you have any C's, I won't serve on the committee).
3. What is your project? (If you are unable to answer this, I won't serve on the committee).
4. Why did you pick this project? (This is an opportunity to tell me more about your likes/dislikes, perhaps a dynamic with your advisor, or to get me interested in your project.)
5. What do you expect my contribution to be to your thesis committee? (Somewhat related to #1, but more about what is the time commitment involved).
I usually turn away about 1/3 but I'll have to refuse more soon because I have too many obligations with the pregnancy and all. I like serving on thesis committees, but I just wish I had more time to do so.