It depends on your filing status, number of exemptions, etc.
In my case, married-filing-jointly with two exemptions (for me and my wife), my AGI can reach ($12600 + $4000 * 2) = $20600 before I start getting taxed.
Of course, that assumes no credits and no deductions. If you've got a lot of both, it's possible to
earn a lot more before paying the first $1 in tax.