Every family is unique. Every folklore fieldworker has his or her own special interests and style of interviewing. Because of this diversity, no single set of questions will successfully elicit folklore from all families. The most useful questions will be those that you develop through knowledge of yourself and your family.
For your initial efforts the following 16 questions may be helpful. Just remember that they are meant to be suggestive, not absolute. Pick and choose among them as you see fit. By all means change the wording to suit your own situation and personality.
[thanks for the lead from @storytellin tweet about PIE: http://www.cimorelli.com/pie/library/intrview.htm]