In my opinion you are asking the wrong question. First of all, you shouldn't ask questions of a professional that you would like to hire before taking a look at their portfolio. That is the complete opposite of what I would do. This is a rule, steadfast, true:

Let the work speak for itself¹

Does the photographer have an excellent portfolio full of the type of work you adore and find exceptional? Then match this with someone who fits into your budget and you have yourself a perfect hire. You can spend all day asking questions, but nothing will ever come close to seeing the finished product, and knowing that the photographer is capable of producing work that you are pleased with.

Once you have identified a photographer with work that most closely aligns with your desires, then you can get into questioning to ensure the match will make sense.

Some questions I would advise would include:

• Pricing, including sitting fee, print fees, packages, inclusions and exclusions
• What to expect at each stage of the process, prior to the shoot, during, and post shoot
• Insurance coverage and professional associations
• How many photographers and assistants will be part of the shoot
• Time allowance and rates for additional time
• Copyright or ability to print images, and the count
• Website presentation, sharing, proofing, access to final images
• Time required to turn around proofs and final images
• Number of venues or "looks" included, if limited
• Access to complete past similar event collections
• Use of backup equipment and "disaster" processes
• Who will actually be shooting, the owner or associates
• Who photographs the engagement session, and will it be the same person(for weddings)

Of course you will want to see, read, and sign a contract to set all items in stone. Make sure to ask any questions on items you do not understand or need clarification on. A proper contract protects the photographer, client, and guests from a variety of issues. As a client it is just as important to demand one as a photographer to use one.

Based on a comment to the original question, if you are interested in the photographers personality(which you should be), I would advise a 1 on 1 in person meeting over coffee before any shoots take place. The reasoning for my tip above around asking who will photograph the engagement session, stems from my belief that for a very critical "once in a lifetime" type event such as a wedding - it is best to have grown comfortable with the same photographer during at least one previous shoot. The engagement session for a wedding is a great time to get accustomed to each other, from both sides of the camera. If your personalities are completely incompatible, this is when you will find out with some certainty. Leaving this determination until the day of your wedding is not advised if at all possible. I also believe that to come to a solid conclusion, the only way to do this is by trial, with a real photo shoot or at a minimum an in person meeting. If the shoot is somewhat less crucial and could be reproduced such as a business headshot, these steps are not nearly as crucial.

You will find a theme throughout this response. Photography is a visual form of art, so seeing the results is of utmost importance. The questions are really only secondary to finding a photographer who is a perfect match for your needs.

¹One great image in 10,000 shots does not constitute "work", see details further in answer.