Yes, you do (at least in the U.S.). But because of the standard deduction of $6,350 (for a single person), and the personal exemption of $4,050 (these are 2017 numbers), you don’t have to pay any tax on the first $10,400 of earnings. So, if interest from savings is your only income, you won’t have to pay any taxes anyway (unless it exceeds $10,400). In fact, if your taxable income is low enough, you don’t even have a filing requirement.
And for this year, the standard deduction amount will be approximately doubled.
@LuckyGuy Technically, you do have to report interest income even if it’s less than $10, but most people get away with not counting it because the bank does not report it to the IRS if it’s less than $10.
But it also gets complicated because there’s also certain kinds of interest that’s not taxable. That’s another story…