Charles Babbage, father of the computer, once envisioned a machine that can calculate mechanically. Called Difference Engine, the machine was never built, until lately.
Wired has a nice gallery of one built for Nathan Myhrvold, a Microsoft millionaire, which will be displayed at the Computer History Museum (the first Engine was built in 1991).
It was said that Ada Lovelace wrote the first computer program for the Babbage's other machine, the Analytical Engine. Yup, the programming language Ada was named after her.
The machine was featured in a novel of the same name by Bruce Sterling and William Gibson.