Although buying a pre-built LED matrix is quick and easy, you can learn a lot by building your own - as Alex Bowen knows, having completed exactly such a project for a microcomputer circuits class he is taking. His LED matrix project, brought to our attention via Hackaday, uses an 8x16 grid for a total of 128 LEDs, all inserted into a sheet of perfboard. The driving logic is, naturally, running on an Arduino Uno, expanded using a pair of 74193 counter integrated circuits (ICs). This means only three pins on the Arduino are tied up, leaving the rest free to provide control for a Tetris-inspired falling block game which takes full advantage of the tall layout of the matrix.
For the electronics aspect, I wanted to create a circuit that could wrap up some complex functionality into a simple interface back to the Arduino microcontroller. The eventual design led to the decision to build an eight-by-sixteen pixel LED matrix.