US freight railways receive no subsidy. Oh, you meant passenger railways?Then you'd probably be looking at Japan.
Parts of the UK rail network that require no subsidy when allowing for all costs including infrastructure and upgrades:
SWT
VTEC
The Thameslink / GN part of GTR
Parts that nearly do, and on current forecasts will do in the next few years:
Greater Anglia
c2c
The rest of GTR
VWC
With Southeastern not far behind
The above represents well over half the railway in terms of both income and passenger miles. Within a few years it will be turning a profit.
The big subsidy goes to Scotrail, Northern, Wales, and (in passenger miles terms) London Overground and Merseyrail.
Clearly then there are ways of making a UK railway profitable, however that would be rather undesirable, for the users of the most subsidised railways at least.