Everybody gave such good advice and I just want to say that when I adopted Elvis and Danny, the lady asked LOTS of questions, which also made me feel comfortable that the cats had been well taken care of by her and her volunteers and that she really cared about their welfare.
A few things she asked me:

-whether or not I had screens on my windows and whether I intended to have them as indoor or outdoor cats. (particularly for Elvis, who had been previously adopted and was allowed to wander and got lost)

-whether or not this was my first time having a cat. She said that this was because she was willing to offer any advice and/or information I needed.

-she requested that we exchange phone numbers/e-mail addresses so that she could contact me for updates. I thought that this was a really good idea and have already e-mailed her pictures of them. She really seemed to appreciate this.

-*VERY IMPORTANT* and already brought up by Leah-asked questions about previous pets who had died. She told me that one guy tried to adopt a cat from her and said that his previous cat had died of "old age", but then he mentioned later in the conversation that the cat had been "two or three years old". SHADY!! Needless to say, she did not let him adopt the cat he was interested in.

A good idea is to try and have a long, relaxed conversation with the person who is seeking to adopt, and try to talk about different things, (eg:job, hobbies, lifestyle) so that you can get a feel for the person and make sure there are no contradictions in their stories. A person who is sincere will seem comfortable and is not likely to become offended by your questions or to become nervous or anxious to leave right away.
Be sure to tell them that they can feel free to contact you should they have any questions or concerns in the future. This is good because it opens lines of communication and hopefully, the person will respond by giving you updates in the future.

Good luck!