Believe it or not, the IRS and most states treat unemployment as taxable income. If your taxable income (including your unemployment income plus any other sources of income) exceeds the filing thresholds for federal (and most states') returns, at least some of your unemployment income can be taxed.
As part of entering all your sources of income in TurboTax, enter your unemployment income from Form 1099-G. We'll figure out how much of your unemployment income (if any) is taxable by the IRS and your state.
Keep in mind: If you're still collecting unemployment, fill out Form W-4V, Voluntary Withholding Request to have 10% withheld for your federal taxes so your tax bill won't be as high next year. After printing and signing the form, make a copy for your records and send the original signed form to your state unemployment office.