Great questions are remembered because they stick with us for a reason.  I participate in a Twitter chat every Sunday morning that usually has about 10 questions and the first one is usually the same format with a little different content.  It is "When you think about or sit with (topic of the day) what feelings does it evoke or what comes to mind?" And we are off and running for a full and rich hour of Q &amp; A and conversation.  This is similar to Mary Schaefer's comment above.  Another question I liked to ask was, "What question haven't I asked that would be helpful?"  That was intended to elicit more information   When I was given a choice between either/or I often tried to see if I could switch it over to both/and unless it was a choice between something desirable and undesirable.
My most favorite question of students (and teachers when appropriate) was, "Is this your best work?"  That usually resulted in a rich conversation about how it could be better.   I have a story, for another time,  that illustrates how that works to get better writing or research from a student, or a colleague.  Asking the right question does take people farther and deeper and such a worthwhile investment of time for mutual benefits.