General:
* Underground
* Metro
* Tube (UK)
* Underpass (for a pedestrian walkway)
* Tunnel
* Rapid transit
* Mass transit
* Public transportation
Informal:
* The train
* The underground
* The tube (UK)
More specific:
* Subway system
* Rapid transit system
* Underground railway
* Metro system
The best synonym for "subway" depends on the specific situation and what you want to emphasize.