Do you have to pay taxes on a settlement from a personal injury lawsuit?

It depends on what the payments are really for. Damages received for personal physical injury or physical sickness are generally NOT taxable. If it is to replace something you actually lost, like an arm, or eyesight, etc...then it isn't taxable. If it is to replace income that you would have made, then it IS taxable (just like the income would have been).
Punitive damages ARE taxable. Damages for emotional distress ARE taxable except for amounts that were used to pay for actual medical expenses (but obviously, those espenses them can't be used as a deduction in your return).