The Amiga is a fascinating system. At the time, it had excellent graphics and sound, roughly equivalent to a Sega Genesis game console, the A500/600/1000/1200 boxes even sharing the same CPU. Because of these capabilities, it was a popular home computer with a LOT of great games. The other application they were particularly good for was video since they had native support for NTSC and PAL video formats. A great many TV studios used Amigas for video overlay graphics and video switching, right up until the transition to HD.

These days there is a really cool open source clone of the Amiga http://en.wikipedia.org/wiki/Minimig

I built one of these recently and have a few extra blank PCBs left if anyone is interested. This is NOT a beginner project though as it's almost entirely surface mount, including the 208 pin FPGA. It took me several hours to assemble it by hand. Ready-made units are available but they're a bit spendy. There is also a build that will run directly on the Altera DE2 FPGA dev board, that one uses a soft core 68000 implemented within the FPGA while the original Minimig uses a real 68k chip.