One funny thing to do which uses all 20 pins of an Arduino UNO and a bunch of LEDs is an LED cube. I found it on Instructables and thought it would be a good value addition to my new workplace. I had just quit IISc and was about to join MathWorks in about a week's time then. So, went and bought 70 blue LEDs and spent 2 days wiring them up in layers of 16 LEDs each. Each layer has a common ground.
And there are 4 layers. So, 16 pins are used to index amongst the LEDs in one layer and 4 pins to index the layers themselves. The result is a cube, which needed persistence of vision to index LEDs which have both different layers and different columns within the layers. This requires a bit lesser amount of coding as compared to the 12 pin solution, which requires PoV to make anything glow.
I assembled the layers one on top of the other and soldered them all to a perf board. Hooked it all up to 20 berg connectors (male) and mounted it atop a clear plastic box. Inside the box is a cheap Arduino clone which handles the LED addressing. A cheap L293D motor driver breakout board handles the layer addressing as each layer would output much more current than what an Arduino can safely sink (as it sources from 16 pins of the Arduino). Below are a few images of the build along with a video. The code used in the video is from the Instructable http://www.instructables.com/id/LED-Cube-4x4x4/.
Incidentally, when I visited MathWorks head office at Natick, MA, in march, I found a much bigger version of the LED cube displaying the MATLAB logo at the entrance of the AH1 block.
