The excellent Eric Crampton writes to me:
If you find any more, let me know. Ones I've found so far:
What is the meaning of life?
What is the velocity of an unladen swallow?
How many roads must a man walk down?
How much wood could a woodchuck chuck?
Why did the chicken cross the road?
How many angels can dance on the head of a pin?
He blogged this experience, along with the answers he got, here. WolframAlpha also tells us that angels have no extension and therefore an infinite number of them can dance on the head of a pin.