I'll use my interview from yesterday.
I asked one interviewer about the summer research fellowships at their school. She is a PhD with an active lab on genetics research for neurodegenerative diseases. I gathered that there are approximately a dozen spots per summer from their website, and I know that there are some recommended electives for students who want to participate in research--another tidbit I found on their website. I asked the faculty what other criteria do they use to assess students for these fellowship spots and generally how competitive they are. I also asked about the application procedures and timeline for the fellowships. I did not find this information on their website, and my student tour guide wasn't sure as she has not participated in the summer research.
I also asked the medical doctor faculty to tell me more about one of their community outreach programs with elementary school children and their international healthcare agendas. These items were briefly mentioned on the website and/or during the introduction and tour. But I wanted more in-depth details. He told me about this new clinic that will soon be in operations, and I remarked that it is a very exciting development. He noted my enthusiasm, and he said, "'Exciting' is definitely the right word." I also wanted to know about alumni involvement in these domestic and global health endeavors.
I also want to add that you may want to take the advice from these forums with a grain of salt, with my advice included, just to be fair. Some of these people are extremely socially inept, anxiety-ridden people who come off as decidedly awkward, and it's probably not the best idea to follow their cookie-cutter style. Just be yourself and be natural. If you have questions, ask them. If not, thank the interviewer graciously and leave. Your questions or lack of questions at the end is not going to make a bad interview stellar, and neither will your decision regarding the questions derail a great interview. Good luck, and have a good time!