Subsidies can take many forms. Of course there are direct subsidies (Airbus, Boeing, etc.) and these are generally disliked. There are tax break incentives, which almost every big business in America gets. Obviously there are tons of small business incentives and employment incentives and so on.
But there are also more subtle and indirect form of subsidies.
China (and other asian countries) are big fans of the "business development zone" ; these are areas they construct for certain industries, provide tax breaks, and build up infrastructure for power, transport, etc.
Government paid health care is perhaps the biggest subsidy any country offers. It's a general subsidy for employment (notably, not for business). In the American model, employers pay for health care - only for employed people. With government paid health care, the employers are still paying for health care (through taxes) - but they are paying whether they employ the people or not.
To make that more clear - imagine a system where everyone was paid $100k by the government, and then corporations had to pay taxes to cover that - whether you were an employee or not. Then there's no such thing as "saving money by laying people off" ; the cost per employee is the same whether you hire them or not, so you may as well hire them. Obviously it's too much of a market distortion for the government to just pay all of everyone's expenses whether they are employed or not, but paying some amount regardless of employment amounts to a subsidy for employment. The more basic social welfare of a person is paid by the government from the general tax fund, the more incentive there is to hire people.
So social welfare (health care being the biggest one) is actually a subsidy for local employment. There are other things that reduce the cost of an employee, such as government child care, good public transit (allows you to pay less because employees don't need cars),
Another big one is education. But of course subsidized education is a form of development of a local business resource (people). Some countries have well developed industry-eduction partnerships to provide students with the skills needed.
I believe that one of the problems in America is that we are in fact engaging in heavy protectionism to this day, but we are not doing it in a very smart way. Defense contractors probably get the biggest subsidy (actually I take that back, finance gets the biggest subsidy by a huge huge margin; finance has been getting around a trillion dollars in direct subsidy while defense only gets a few hundred billion), but so does aviation, mineral/mining, lumber, agriculture. They are generally in the form of direct subsidies (eg. have some free money), which is a very bad way to do it. Direct subsidies tend to go straight into rich people's pockets, they don't promote employment. Subsidies can be crafted in more clever ways, and the best way is not to favor one particular industry over another, but rather to favor employment over outsourcing and let the market decide what type of employment is best.
Of course the US government does heavily subsidize certain behaviors, so the idea of subsidy to affect the market is not at all exotic. The subsidies for real estate investment are massive; even ignoring TARP and the FM's and such, the mortgage interest deduction and capital gains exclusion are huge behavior modifiers for very questionable benefit. The lower capital gains tax (vs. income tax) and dividend tax rate are huge subsidies for investors. And of course the tax code in general is a huge subsidy for corporations (vs. individuals) and particularly for multi-national corporations. Why are we massively subsidizing all those things, and not employment and local business?