What's the situation? What is your relationship to the person you're trying to get to know well? Significant other? Friend? Boss? Colleague? Business partner? Tenant?
A. Significant other?
How do you feel about having children?
What are your views on raising children? Do you believe in strict discipline or a more open, creative, forbearing approach? And so on.
How do you spend your free time?
C. Boss (One doesn't usually ask questions of the boss, does one?)
D. Colleague (This really does depend on the enterprise you're going into to a certain extent)
What are your views about failure?
E. Business partner
Same question: What are your views about failure?
Do you have any pets?
Hope that helps. Take it easy. :D