All forms of transporation are subsidized, and most forms of transporation should be subsidized. This is because transporation networks are public goods, whose benefits (and some costs) spill well beyond their borders, and cannot be captured by their users or owners. Transportation networks enable our defense and disaster response capabilities, boost our economy and dramatically property values. On the downside, they result in physical separation (thus making human-powered transporation difficult or impossible), pollution, noise, and congestion. On balance, their spill-over effects are hugely positive, and because of this, "free markets" would significantly under-supply them. Additionally, "free markets" would even fail to properly manage the networks they did build, as in far too many cases, much of the network would be a natural monopoly.
One popular myth is that because we have gasoline taxes, roads "pay for themselves" and are not subsidized. This is not true and has never been true. The gas tax is far too low to pay for all of our road spending. Depending on how one does the figures, user fees such as gas taxes now only cover 50-70% of the money spent on roads in the US. Compare this to Amtrak, which only received $562 million in subsidies in 2011 out of a budget of over $3.7 billion. Yes, Amtrak is less subsidized than the typical American road. Yet one of the first first complaints about HSR that most detractors bring is that it requires subsidies, while they ignore the fact that the competition is subsidized as well! Also note that most of the HSR systems in the world are profitable, despite the subsidies for their competitors. Even our beloved Acela, the closet thing the US has to HSR, is profitable.
Subsidies, however, extend far beyond simple cash transfers or targeted tax breaks. The biggest subsidies most industries possess is the right to externalize costs - to pollute, make noise, or otherwise inconvenience their fellow citizens without a reasonable mechanism for compensation. All transporation systems have some negative externalities such as pollution, noise, congestion, accidents involving non-users, security requirements, and physical separation. However, HSR has much lower externalities than its primary competitors, driving and flying. Drivers externalize a lot of danger (some 5000 pedestrians and cyclists are killed by drivers each year), a lot of noise, consume a disproportionate share of our police enforcement, and pollute about four times as much as HSR per passenger mile, while concentrating that pollution in our highly populated areas. Airplanes pollute about as much as cars per passenger mile, devalue the land around airports for miles with their noise, and again consume a lot of law enforcement dollars. Both of these systems are critically dependant on oil, which is a major national security concern and is a likely driver of a fair portion of our military spending. Add it all in, and you would need a gas tax something like $2.00/gallon (vs less than $0.50 in most states) in order to appropriately incorporate all these costs into the price of gasoline. Certainly, $5.00/gallon gas would make driving and flying look a lot less viable.
HSR, in contrast, has fewer negative externalities. The land value boost around stations is enormous, offsetting any losses for land near the tracks. Noise is modest relative to automobiles, particularly trucks and emergency vehicles, and pollution is not only just a fraction of what is released by cars and planes but is also generally released in low population areas where power plants are located. HSR also reduces congestion at both the roads and airports it competes with.
The "free market" cannot work when there are so many externalized factors, both postive and negative. It will simultaneously under-supply everything, monopolize what it does supply, and supply the wrong balance of options because the externalities are not symmetric. We have to approach the decision on how much capital to allocate to transporation, and how much to allocate between various options, using an entirely different conceptual framework. Given the success of HSR abroad, and the virtually inevitable rise of oil prices over the coming decades, HSR stands out as a clear path forward to providing our transportation needs for the next century and beyond.