There is a short answer, but as the remainder of this answer explains, it isn't a very meaningful one because there are lots of other material considerations to take into account that the narrow short answer omits in a manner that is misleading when making international comparisons.
According to the Washington Post in 2013, the U.S. had the most progressive federal income tax system in the OECD (which includes developed nations only).
Considering Taxes and Transfer Payments Together
This is complicated by the fact that most other OECD countries make more generous transfer payments to the poor than the U.S., so if you combine taxes and transfer payments, the U.S. is 12th as the Brookings Institution explains.
Basically the same data is discussed by Greg Mankiw, an economist, at his blog, which discusses the concerns about transfer payments and the selective set of taxes that are included and excluded in that data set.
In concrete terms, how does this play out?
A hypothetical self-employed middle or upper middle class person in the U.S. may have lower direct tax bills, but also has to pay out of pocket for health insurance every month (often more than their mortgage), has to set aside private savings for retirement, and has to pay hefty sums to send their children to preschool and college. But, that person usually would have their children's K-12 education provided more or less free of charge.
A hypothetical Scandinavian middle or upper middle class person may have higher tax bills, but gets free health care, a generous pension when they retire through the social security system of their country, and free preschool-16+ tuition when their kids need education.
You really can't meaningfully compare the extent to which government intervention is redistributive (which is the point of knowing if a tax system is progressive or regressive) without have a firm grasp of the distribution of the transfers go are paid for with those taxes.
It is also necessary to have a good command of the details of a tax system to evaluate if it is progressive or not. Tax rates are not the whole story. For example, a VAT system that zero rates food tends to be progressive, while one that does not tends to be mildly regressive.
General Trend Beyond The OECD
Of course, the OECD makes up only a small share of all countries in the world. All sorts of varied sets of tax rates exist around the world. Overall tax revenues also vary wildly from 1.4% of GDP in the United Arab Emirates to 50.8% of GDP in Denmark. Apart from an exception for natural resource rich monarchies discussed below, generally speaking, less developed countries tend to collect a smaller percentage of the GDP as taxes than more developed countries do.
The U.S. is still more progressive than many less developed countries even this broader tax and transfer measure of a progressive tax system. In general, less developed nations tend to have more regressive taxation than more developed nations.
No Representation, No Taxation Economies
A notable exception to this general rule applies to monarchies in natural resources rich economies like Saudi Arabia and Brunei, where the predominant political economy model is no representation and no taxation at all for ordinary citizens, accompanied by substantial transfers to less affluent citizens. (The only income or consumption tax paid by Saudi Arabian citizens is a 2.5% corporate income tax paid by corporations on the percentage of their income attributable to Saudi Arabian owners. Foreigners in Saudi Arabia are subject to significant taxation at rate of up to 85%.)
In some sense, these monarchies have the most progressive taxes in the world. All costs of government are paid by the richest family in the country and nobody else pays any meaningful taxes, while lots of people get government benefits.
How Should One Treat Revenue From State Owned Enterprises?
Another methodological difficulty is how to treat state owned enterprises and resources.
For example, in the United States, a large share of grazing land and mineral rights in the American West are owned by the federal government and leased to private sector ranchers and oil and mining companies. Are those lease proceeds effectively a tax, or are they something different?
This is a relatively minor issue in the U.S. economy, but is a much bigger one in a country like Mexico, which has a largely state owned oil and gas industry which makes a substantial contribution to the economy. In many socialist and communist countries whole industries that would be in the private sector elsewhere are government owned.
For example, a couple of decades ago, in Singapore (often inaccurately touted as a capitalist mecca), something like 87% of residential real estate was government owned through the main government owned housing program (additional percentages were leased under other programs) and almost everyone in the country was a tenant. In that context, how do you economically distinguish between rent and tax revenue and transfers, when rents weren't set strictly on a market economy basis?
Similarly, how do you evaluate the tax burden in the case of defense contractors in China who are mostly government owned?
In a hypothetical economy where the state owns all means of production, is the effective tax rate 100% or 0% and how should that be allocated to different parts of the income distribution?
Federal v. Inferior Subdivision Imposed Taxes
Also, considering only federal income taxes, but not state and local taxes, such as state sales taxes, distorts the overall extent to which a tax system in a country is progressive.
On average, state and local taxes in the U.S. are more regressive than federal taxes. Measuring only national taxes and not state and local taxes is problematic, because countries differ dramatically (and not really with any rhyme or reason in terms of level of development, or formal political federalism, or overall extent of progressive taxation) in which levels of government collect taxes and spend money.
Sometimes, even defining which level of government is collecting taxes isn't obvious. For example, in Germany, a lot of substantive law is established at the national level, but administered by the states, so that even federal taxes would frequently be collected by state tax collection departments.
Direct v. Indirect Taxes
Measuring indirect v. direct taxes and determining the incidence of indirect taxes is also a much bigger issues in less developed countries, because indirect taxes are often easier to a weak government to administer than direct taxes.
For example, many small island nations, such as those in the Caribbean (e.g. Haiti), get most of their government revenue from customs duties and have very little direct taxation. One of the reasons that tax havens can afford to forgo government revenue with tax breaks is that the taxes they refrain from imposing aren't part of their tax base anyway.
The extent to which direct taxes are progressive is pretty much irrelevant and ill founded in a country where the lion's share of tax revenue is from indirect taxes where the incidence of taxation is potentially a matter of debate.
If nobody is paying more than 2% of their income in direct taxes, the incidence of the indirect taxes matters far more than the extent to which the direct taxes are progressive or not. There isn't much functional social equity difference between a country where the rich pay 1.5% of their income in taxes while the poor pay 0.5%, and one in which everyone pays 1% of their income in taxes, and one in which the poor pay 1.5% of their income in taxes and the rich pay 0.5% of their income in taxes.
On a combined direct taxes and government transfers basis, in a typical Caribbean island tax system, almost everyone but the very rich receives more in transfers than they pay in direct taxes, in theory, creating one of the world's most progressive tax regimes.
But, there are good economic arguments that in these economies the actual incidence of customs duties is quite regressive and is economically equivalent to a U.S. style retail sales tax, because services are often not subject to customs duties, while goods (even essential goods that are exempt from many U.S. style retail sales taxes) are subject to customs duties in these countries.
This principle applies even to the U.S., historically. Prior to the U.S. Civil War, the federal government was predominantly financed with customs duties. But, when the Civil War made it necessary to greatly expand the size of the federal government, it began to impose substantial direct taxes. This was rolled back for a while after the Civil War, but reinstated during World War I, after which the new taxes on incomes and estates were never repealed, and both the scope of the federal government's activity and the amount of federal direct taxation dramatically increased again with the New Deal and then with World War II.
One of the dominant issues in the first nine decades of Congressional debate in the United States was the question of the incidence of U.S. customs duties, which the South argued burdened them more, and other states argued were more equitable.
This is a problem, because economists differ widely on even the most basic questions about the incidence of indirect taxes, such as who bears the economic burden of corporate income taxes and customs duties.
Intentional Inflation As A Form Of Taxation
A similar separate and significant issue is how to treat the economic consequences of a government's decision to have high rates of inflation. Economically, this is a serious tax on people with assets and fixed income streams denominated in the national currency, and a major transfer of wealth to people who own tangible assets, and people with debts denominated in the national currency (including a transfer from holders of government bonds to the government).
Hyperinflation (such as that seen in Venezuela where inflation was 700% in 2016) and practices like the recent declaration in India that 500 and 1000 rupee notes of paper money no longer have any value, can be equivalent to confiscatory taxation schemes and disproportionately affect people who are rich in monetarily denominated wealth.
Usually, these currency manipulations are themselves progressive in economic impact, although the harm they do to the economy in general, makes it possible for them to have net regressive effects depending upon which sectors of the economy are most affected and upon which sectors of the population hold wealth denominated in the national currency.
Taxes Imposed v. Taxes Collected
Another big issue is whether estimates are based on taxes on the books, or taxes actually collected. Some taxes (e.g. Social Security payroll taxes in the U.S.) have near 100% compliance. Other kinds of taxes are collected less reliably (for example, self-employment income in circumstances not subject to information reporting have low levels of compliance).
For example, one of the important causes of the sovereign debt crisis in Greece was the fact that Greece has the lowest rate of collections on taxes that are formally imposed in the E.U.
