The following post from the "Everything Seminar" blog would make an excellent lesson in my opinion (link is below). It starts from a simple, but clever "hats puzzle" and then presents an infinite version of the puzzle which is solved (quite amazingly and beautifully) using the axiom of choice. It exemplifies the gap between what we expect to happen and what actually happens which is encountered in mathematics from time to time. Also, you don't really need to introduce any complicated concept, only describe what an equivalence relation is. The mere definition of an equivalence relation is beautiful mathematics in my opinion and the way in which such a simple concept can be used to solve a difficult (impossible?!) problem as above shows how interesting and intriguing mathematics can be.
The relevant post is here: http://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong/