The New York City Subway is a rapid transit system owned by the City of New York and leased to the New York City Transit Authority, a subsidiary agency of the Metropolitan Transportation Authority. It is one of the oldest and most extensive public transportation systems in the world, with 468 stations in operation (421, if stations connected by transfers are counted as single stations). Overall, the system contains 209 mi (337 km) of routes, translating into 656 miles (1,056 km) of revenue track; and a total of 842 miles (1,355 km) including non-revenue trackage. In 2011, the subway delivered over 1.64 billion rides, averaging approximately 5.3 million rides on weekdays, about 3.0 million rides on Saturdays, and about 2.4 million rides on Sundays. (from Wikipedia)
The subways are called trains and run north, south, east and west.
Subway Map (PDF)
MTA
Expect this.