For much of this year we've been hearing that 47% of U.S. residents get away with paying no federal income tax. More precisely, that was the fraction of households with no net income tax liability in the year 2009, when unemployment reached a peak and temporary tax breaks in the Obama stimulus that have since expired reduced taxes for almost everyone with earned income.
In more normal times about 40% of households, including many retirees, students, the disabled, the poor, the very young, and so on don't have enough earned income to to exceed their total deductions and exemptions or else benefit from the Earned Income Tax Credit and the Child Tax Credit for working families. Other breaks are available to those with high income.
People who pay no federal income tax almost always do pay other federal, state, and local taxes, many of which tend to be regressive, hitting low income people harder than the well-off. Almost every working person pays significant federal payroll taxes, which are the most regressive of all, with the first $110,100 per year of income taxed at a much higher rate than the portion of earned income over that amount, and investment income is exempt from the tax.
Taking all taxes into account, the U.S. system is just barely progressive, taxing high-income people at a rate only a little higher than low-income people. High-income people do pay a large share of all income taxes, in considerable part because income in the U.S. is so skewed. For example, the top 10% of U.S. residents took in more than 42% of of all personal income last year.
Here are a couple of data-filled articles you might find interesting:
"Misconceptions and Realities About Who Pays Taxes" from the Center on Budget and Policy Priorities.
"Note To Romney: Overall Share Of Taxes Largely Aligns With Share Of Income" from Think Progress.