Merriam-Webster's Word of the Day for November 08, 2008 is:

conundrum • \kuh-NUN-drum\  • noun
1 : a riddle whose answer is or involves a pun 2 a : a question or problem having only a conjectural answer*b : an intricate and difficult problem

Example sentence:
Ideally, students in an ethics class are encouraged to really wrestle with moral conundrums.

Did you know?
The exact origin of "conundrum" isn't known with certainty. What is known is that the word has been in use since the early 1600s, and that it had various spellings, such as "conimbrum," "quonundrum," "conuncrum," and "quadundrum," before the current spelling was finally established sometime in the mid-17th century. One theory of origin suggests that the word was coined as a parody of Latin by students at Oxford University, where it appears to have enjoyed particular popularity in its "word play" or "pun" sense. While the prevalent sense in this century is that of the seemingly unanswerable question or problem, frequently applied to heady dilemmas involving ethics, sociology, or economics, the word is sometimes so loosely applied to anything enigmatic as to be synonymous with "puzzle" or "mystery."

*Indicates the sense illustrated in the example sentence.