The following are my three favorite logical puzzles of all time. Don't even bother trying them if you don't have a firm grounding in set theory and modal logic.
Logical Puzzle #1: A Cretan says "All Cretans are Cretans." Suppose he is telling the truth. Does it follow that all Cretans are Cretans? Really? All of them?
Logical Puzzle #2:. You must transport three sheep across a river, but your boat can hold only you and one sheep at a time. How can you transport all three sheep across the river so that none of them eat one another?
Logical Puzzle #3:. You visit the Island of Knights and Knaves. Knights always tell the truth on weekdays and when it is cold outside. Knaves always lie on weekends and when it is warm outside. What time is it?