The first attempt to build a subway in New York City wasn't like the underground system we have today; it was going to be pneumatic.
The system, built in 58 days in 1870 by Alfred Beach, managed to stretch 312 feet in just one tunnel. As this excellent io9 article explains, the system didn't really pan out.
But it was ambitious, and it was extraordinary. Surely you know a subway system (whether it be one that was completed, planned, or only imagined) that was even more daring.
Photo Credit: nycsubway.org