That really depends on just how badly one needs the job in question.
The more you need the job, the fewer questions you're likely to ask.

One time years ago a headhunter recruited me for a senior dev position. I drove 30 miles to the interview and found myself facing a panel of a half dozen people asking pretty idiotic questions about how one administers a database.

After about 5 minutes of this I said, "Am I being interviewed for a database administrator position?". They answered yes. I said, "I was told this was an interview for a senior dev slot. I could be a decent DBA, but it's not my core competency or my core interest." They looked at each other and then the head honcho said, as if it had been MY mistake, "Er, thank you for being honest with us." And I drove 30 miles the other way, back home, and never heard from the company, or the headhunter, again.

Based on that experience, one of my first questions would be to confirm that I'm actually being interviewed for the correct position Happily, I haven't had a job interview in the ensuing 15 years, or even very many before that. Except for a brief period right after I relocated from the midwest to Arizona, I've been entirely self-employed.

Another variation on this is that headhunters recruit me all the time for jobs that I'm not remotely qualified for, or that require travel or on-site work that I make clear up front I'm not open to. There's no targeting at all, they do an ill-conceived keyword search of resumes in their database (many, like mine, are there because I posted it once online 20 years ago) and blast an email to all that kinda-sorta match.

Finally there's this choice tidbit: in 2002 I saw a job listing that listed among its requirements, "at least 3 years experience with the .NET framework" -- a product which had been on the market about 3 months at the time. This illustrates the disconnect between the Human Resources department, which always has a dream list of ideal qualifications which, even if they were possible, would be worth way more than they're willing to pay for if concentrated in any one person -- and they don't understand what the qualifications mean to begin with. The predictable result is that everyone lies about their experience and expertise and generally get the job by telling interviewers what they want to hear.

Which leads me to my other implicit question: "Do you guys have the vaguest idea what you're doing?"

I actually took a job, on purpose, with a client that didn't know what they were doing, based on the ridiculous rate of pay and my calculation that the job would last 18 to 36 months before they either ran out of money or I ran out of patience. I left that job in 2006 after about 20 months and haven't quite matched that hourly rate since. They ran out of money just as I was running out of patience. I wrote a nice finished system that they never deployed because the VP in charge couldn't maintain it personally for lack of relevant knowledge and experience with the technology. The whole thing was just a front to say they were modernizing a system that everyone in the company was frustrated with. Considering the people I hired to help out and various incidental expenses, I figure they blew a cool million on a system that the VP never actually planned to use.

Such things happen in business ... it hones one's sense of absurdity and irony at least.

Is drinking allowed? Do you put pineapple on pizza? Do you have a daughter? What's her cup size?

Who held this position previously?
How long did they have it?
What was their background experience/education when they were hired?
Why did they leave and what do they do now?
Can you provide me a comprehensive job description?
What is the organizational structure?
To whom would I be reporting?

How long have you worked here?
Why do you like this company?
If you were the CEO, what would you do differently?

1. What are the goals for this position in the first six months?

2. Who would be my supervisor?

3. Why did the last person in this person leave?

4. When will the position begin?

5. What are the biggest challenges of this position?