What are some of your favorite paradoxes and puzzles?

You know, brain teasers and all that jazz. What are some of your favorites? Have any “solutions” to paradoxes? What puzzles stumped you when you first heard them?

I was just reading the Unexpected Hanging paradox (I originally read it in a book I had in middle school as the “unexpected tiger) and it inspired this question.

One I love is the Monty Hall problem. There are 3 doors on a game show. Two contain nothing, 1 contains a cash prize. You may choose 1 door and then host will then open another empty door and allow you to stick with the door you chose, or switch to the unopened one. Say you choose Door 1. The host opens Door 3, revealing it as empty. You may now either stick with Door 1 or choose Door 2. The fact of the matter is, it’s always advantageous to switch to the other door. But why? I know why, but do you? :P