I find a lot of people ask questions about things like team size, management structure etc. If there are a mixture of responsibilities in the job you might ask what the balance is between them. Sometimes pragmatic and practical considerations like where do most people live who work at the institute (we're an out-of-town campus), how do you get to campus if you don't have a car etc. You can also ask how they plan to train you up, what training opportunities are available throughout your time at the organisation and what opportunities there are for attending conferences.
I've also had people ask about the social aspect of the job, ie I'm going to be upping sticks and moving to a new area for this job, is this the kind of place where I would make friends? Some people see this as taking a flighty interest in non-work aspects the role, I see it as someone seriously considering what their life would be like if they took the job.
I like people to ask questions during the interview. An interview is as much about the candidate interviewing the potential employer as it is about the employer interviewing the candidate. If someone asks no questions, then it feels a bit like they lack curiosity (and what kind of terrible scientist lacks curiosity), or just lack self-interest or drive. I think it's worth having a few standard questions prepared. If somehow all my questions get answered during the interview, I tend to say something like, "I was going to ask about blah blah blah, but you already covered that."
This may be a cultural thing. Western societies being more open expect the candidates to pipe up and ask questions. If you don't have a question that was not addressed during the interview then saying "no thank you" is perfectly fine. Asking a question for the sake of asking something does not make sense.
On the other hand this is your chance to ask any questions (that may not be directly related to the interview) but are important to you.
What genomax said, and I'll add that this is also an opportunity to salvage an interview that may not have gone well. For example, if you have the feeling that you've not engaged properly or as fully as you would have liked with the person with whom you're speaking then you could use this as an opening to branch to a conversation where you can engage with one another more. This can then leave the person with a bit better impression at the end. For such purposes the question doesn't have to be one you don't already know the answer to, though obviously it shouldn't be one you've discussed with that person already.