A few examples of what you might ask:
When is the unit available?
Is price negotiable if applicant has a strong credit history and strong landlord references?
Is there an application fee?
Is there a copy of the house rules (if applicable) available?
Have there been any past problems or defects?
How long has it been a rental?
Does the Owner intend to sell the home in the next few years?
What utilities are included, if any?
Special considerations based on your lifestyle such as: Does property allow for a Dish sattellite system at tenants' expense for installation and removal?
What are the expectations regarding the yard maintenance (if applicable)? Is yard service included and how often?
Have your list of questions written down so you can ask at the time of your appointment. If inventory is low -- which it often is in many neighborhoods -- and you are in a competitive situation, you may not want to barrage them with too many questions early. Instead show them why you would make the best tenant and wait until the property is offered to you. A long list of questions could be perceived as a potential turn off for the Landlord.
If there are any special terms negotiated verbally, make sure it is stated in writing in your agreement or as part of an addendum to your lease agreement.
Happy House Hunting!