One project I've been kind of wanting to make is an LED cube. To illustrate just how awesome charlieplexing is, look at how many output pins you'd need to drive an LED cube of a given size compared to the simple multiplexing I "invented".
|Edge Length||# LEDs||Req. Multiplexed Outputs||Req. Charlieplexed Outputs|
So on the Arduino, where I think I have 12 ports to work with, I could either do a 3x3x3 cube the old and busted way or do a 5x5x5 cube the new hotness way. (Or maybe I have 18-19 ports, in which case it's still 3x3x3 the old way but now 6x6x6 the new way.) But how can you possibly control that many LEDs with so few ports? Read the instructable!
Or read this simplified summary: Basically, you set things up so that every port can be either positive or negative. Then attach your LEDs so that every possible combination of ports lights one up. (Remember that LEDs are one-way valves, so port A being positive with B negative can light one LED while reversing polarity can light another one. Just remember not to cross the streams.) "Every possible combination" of N ports is N *(N - 1), so with, say, 9 ports you can control 9 * 8 = 72 LEDs.
5x5x5 isn't enough to be a 3D display, though. But a larger cube could be decomposed into smaller cubes each controlled by a separate microcontroller. 10x10x10 is probably large enough to show some cool animation, although coordinating 8 microcontrollers might be a pain. Not to mention wiring up 1000 LEDs.