Personality is an important quality to consider when determining who will design your project. The architect you choose will need to work well with many types of people and professions, and most importantly he or she needs to work well with you and the builder/contractor. There are as many questions you can ask as there are published lists. The list I have generated is designed to be simple, from the hip, and a basis for which your relationship will grow.
1. Where did you go to school? We don’t think you care, but apparently the market research says you do. 
If you have any questions about certain schools, leave a comment.
2. What is your design philosophy? Identically aligned with you is not crucial, but agreeable philosophies will ensure your needs are met. A flexible opened mined architect is better.
3. Name one architect who has influenced your work and why? Then do some research.
4. How will you learn what will work best for me? Most architects have their method of getting to the genesis of your needs. Just make sure its discussed early in the process.
5. How big is your firm? This and the next question will determine if they can handle more work and ultimately how much attention you’ll get.
6. How many projects are you currently working on?
7. What kind of music do you listen to? I don’t think there is a wrong answer
but I believe some personal questions can reveal professional attributes.
8. Do you provide cost estimating? If you have a large commercial or public project, a fairly accurate estimate might be important. A small or medium sized firm will probably outsource the estimating, unless they have a design-build operation, then it will likely be done in house. For a small retail or residential project a preliminary opinion of costs might be all you need.
9. What do you need from me? Believe it or not 
you will need to furnish certain information or documents. He or she will be able to determine what you need.
10. Can you recommend a contractor or do I need to find my own? An architect is probably the best resource to find a good reliable contractor.
11. Are you flexible? Most people are flexible but it’s not a bad idea to establish the dialogue early. Be candid with your needs.
12. Do I get 3D renderings as part of your base fee? Seeing a project in 3 dimensional perspectives will give you a better sense of how it will look. At one time this was an extra charge and an expensive one. But the software available today that uses BIM technology has made this much more affordable.
13. Do you provide construction administration 
services? This involves overseeing the construction process once the project is designed and permitted. To put it simply, if you care about the outcome, keep the architect around. He or she knows the design better than anyone, even you.
14. Why should I hire you?
15. How do you structure your Fee? There are many ways to answer this and a topic for another day, but for now it’s important to get the dialoge on the table.
16. Have you worked with the building officials in (insert name of city or town) before? Not critical but if there is an established relationship your project might go that much smoother.
17. What do you do when you are not doing architecture? Some architects can be consumed by their work. It’s just 
my observation, but I would want someone who has other interests, or is involved in other things.