You can find dozens of websites claiming you don't have to pay income tax because there's no law that requires you to. This is not true: The U.S. Tax Code includes provisions that enact the income tax into law. It may, however, be possible for you to arrange your finances so that you don't have to pay income tax, or even file a report. Whether you can do it will depend on your income, and the deductions and tax credits you can claim.
Reduce your taxable income in favor of relying on sources of nontaxable income. You won't pay tax on money you withdraw from a Roth Individual Retirement Account, for instance, and Social Security benefits aren't usually taxable. If you are 70 and you support yourself on those sources alone, it is possible your taxable income is zero. Even if you do earn a small amount, below a certain income level -- which the government adjusts periodically for inflation -- you still don't have to pay taxes, or even file a return.
Take advantage of every possible deduction. Even if you don't itemize deductions, you may be able to write off some of your moving expenses and student-loan interest on your 1040, as well as other categories of expense. If you're self-employed, most business expenses, from mileage to advertising, are deductions, and you can also claim part of the Self Employment Tax you pay. If you itemize, you can write off a variety of expenses, including medical bills, charitable donations and interest on your mortgage. Each deduction lowers your reportable income, and therefore your taxes.
Look for tax credits you can claim. Unlike deductions, which lower your taxable income, you can subtract a tax credit directly off your taxes. The Energy Star credit allows you to claim one third of the cost of a home solar-energy or wind-power system, for instance. The Lifetime Learning Credit allows you to deduct some of the tuition and other college expenses for yourself or members of your family. Some credits will actually refund you money if you can claim more than you owe in taxes; others will have part of the credit carry over to the following year.
There are many financial or legal "experts" with systems for sheltering your income so that the Internal Revenue Service can't touch it. Some of these proposals are valid and legal; some are illegal and some are outright scams. Check with a reliable attorney or financial adviser before you sign up.