One single proposal per answer, most upvoted as of 2013-12-07 (12:00AM UTC) becomes our next challenge!
The winning entry shall be marked as the accepted answer.
Fizz-Buzz-Banana is too easy. Evaluating a poker hand demands a bit more brain juice, and has many ways of turning into spaghetti conditionals that are going to be fun to review.
Oddly this is missing the unachievable Royal Flush (10-J-Q-K-A, all in the same suit), but I didn't look very far for something usable with a CC-Wiki license:
Fizz-Buzz is too easy. Let's stir things up a bit and add a little spice - Banana is whatever you want it to be, and if you want you can add Apple, Orange and Cherry as well.
Specs (for those who need them)
Players generally sit in a circle. The player designated to go first says the number "1", and each player thenceforth counts one number in turn. However, any number divisible by three is replaced by the word fizz and any divisible by five by the word buzz. Numbers divisible by both become fizz buzz. A player who hesitates or makes a mistake is eliminated from the game.