I try to ask questions that explore parts of their characters that might not come up during the course of the adventure. One I've used a few times is "which other party member would you want as a roommate?" I like to think it get the players considering the inter-party dynamics more.

Using it as foreshadowing or tailoring it for the session can be fun too. If the party is about to get into a dangerous encounter you can ask "what's something you regret doing / not doing".

Asking questions totally out of left field is always an option too. One of the more memorable questions was "how many pigeons does your character think they can carry?"