Different people find different things funny and therefore funny questions are subjective; however, one question that people might find funny is, "Do you have any pet peeves?" Another funny question might be, "Would you rather spend a year on a sailboat or a year in a submarine?"
The best funny questions will inspire amusing conversation. For example, with the pet peeves question, the pet peeve itself might be funny and ignite the conversation. Another potentially funny question is, "Do you have any phobias?" or "Would you rather eat a sock or wear a bag on your head for one entire day?"