Question: A town only has one barber (he is male). The barber only shaves all of the people who do not shave themselves.
So who shaves the barber?
Answer: It's a paradox, if he shaves himself then the second sentence would be false because he only shaves those who do not shave themselves. If he does not shave himself, then according to the second statement he must shave himself.
Question: What tastes better than it smells?
Answer: A tongue.
Question: What loses its head in the morning and gets it back at night?
Answer: A pillow.
Question: What two things can you never eat for breakfast?
Answer: Lunch and dinner!
Question: What asks but never answers?
Answer: An owl!
Question: What can you catch but not throw?
Answer: A cold.