I had two phone interview recently. Both are academic libraries. I can't remember some of the questions but here are some I do remember and want to share with you.
1. List three qualifications that you think important for the position
Or why do you think you qualify? Or why apply for the position
2. new trends in this particular area
3. collaboration within the institute
4. experience with faculty/students (diversity), how to develop the relationship, how to determine their needs
5. How to handle unexpected situation
6. give an example of leadership
7. experience with reference, collection development, bibliographic instruction, software, standards (sth relates to the position)
8. Why librarianship
9. Strength and weakness
10. example of your problem solving skills, creativity
11. long-term professional goal
I think it's important to familiar yourself with the resume and try to come up with as many examples as you can to demonstrate how compatible your skills and experience are with the position. I have use a same example to answer two questions.

And more importantly, you are truly enthusiastic about the position.
I am still new to this profession and to job hunting so I don't have too much experience to offer. And I will still be around and asking for suggestions. Thank you for those who helped me with my questions. Wish everyone like me good luck!