-Asking about her family
-look for the presence of siblings, especially younger ones.
-look for healthy parent relationships + a lenient/submissive wife
-pets usually don't mean much
-Education
-Ask her what her future ambitions are. This reveals a ton about the mindset of a woman. Their answers ALWAYS differ tremendously.
-Ask her what her interests are. Not only do you find out if she is compatible, but you can uncover a lot about the personality of a person through their hobbies.
-One that doesn't require any kind of confrontation - watch how she eats her food...does she enjoy it, eat neatly, use her right/left hand, chew silently?
-How does she carry herself? Is she out of it, alert, relaxed, infused into the scenery/people around her, always with someone else?
-Most importantly - how does she treat other people? Does she seek approval, mistreat others, pay too much attention to inconsequential things, more/less superficial than with you?
There's a lot of subtle tests for the male, often not involving direct questions. Just pay attention to the behavior of your girl. By discerning the various aspects of her life, you can get a much better impression as to how the relationship will turn out.