Analytical Engine Emulator
In 1837, Charles Babbage wrote a memoir entitled On the Mathematical Powers of the Calculating Engine. In this paper, he described a machine, steam powered and made of brass, that would be able to store and run general-purpose programs. While it was never fully constructed, Babbage's Analytical Engine was the first computer to ever be designed.
Usually computer emulators are designed to mimic computers that actually existed, but fortunately for the curious, someone has put together a Java-based Analytical Engine Emulator for the really-retro computing enthusiasts to play with. I haven't got the time nor inclination to write programs for it myself, but I think Babbage would appreciate his idea being brought to virtual fruition.
Speaking of programming the thing—although it was never built, it did have programs written for it. In fact, the very first was written by Ada Lovelace, who thus has the distinction of being the first computer programmer. It is sadly ironic that a field pioneered by women such as Ada and Grace Hopper, inventor of the first compiler, now finds itself with very few women practicing its arts.