Everything that has 3D word attached seems cool today. So LED displays aren’t exception. Easiest way to make a 3D display is to build a LED cube.
This LED cube is build of 512 or 8x8x8. It may look quite small resolution, but keep in mind that each LED has to be hand soldered in to nice cube and this is quite time consuming. Another thing is that more LEDs require more power to drive and more I\Os. Microcontrollers have limited number of pins so there are eight 74HC574 latch registers used. Each of them is decoded with 74HC138 chip. This gives 64 programmable pins out of 8+3. Add 8 more pins and you can scan through all of them. Instructable gives really detailed instructions on how to build one and program it.