Not if they have a tax-exempt foundation with which to shelter the income.
well apparently not many do since:
The Top 50 Percent of All Taxpayers Paid 97 Percent of All Income Taxes; the Top 5 Percent Paid 57 Percent of All Income Taxes; and the Top 1 Percent Paid 35 Percent of All Income Taxes in 2011
The taxpayers with 6-figure incomes pay a ton-load of taxes. The ones wealthy enough to set up foundations and 501(c) "charities" are another story. Have the 501(c)'s pay corporate taxes on their investment income. Tax the income from Harvard's endowment.
That hasn't been true since the Reagan administration. It used to be that you could put all of your assets and all of your income in a non-profit foundation, borrow any funds you needed from the foundation, then just never pay it back. Totally tax exempt! It only cost you a law firm to manage the foundation and hand over the money whenever you wanted it.
During the Johnson administration a law was enacted requiring all non-profit organizations to practice fund accounting, which is an accounting method that traces every dollar from income to expenditure without any common accounts to obscure where funds come from or where they go.
During the Reagan administration a law was enacted to make unpaid debts taxable. That pretty much ended the party for tax exempt foundations. Only the Kennedy's escaped. They got a special rider added to the bill to exempt their foundation.