Yes, they often are, but it depends upon the type of settlement. The settlement type will be listed in your Final Settlement Agreement.
Physical injury or sickness settlements (dog bites, mesothelioma, etc.) are non-taxable and don't need to be reported unless you deducted medical expenses related to the injury on a previous tax return and you received a tax benefit from the deduction. In that case, report the medical expenses related to the incident as miscellaneous (other) income.
Punitive damages are taxable except in certain wrongful death cases, as are awards for employment discrimination and injury to reputation (libel, slander, or defamation).
Emotional distress and mental anguish settlements are taxable, but only on the amount above and beyond the undeducted medical costs for treatment of the distress or anguish. You'll need to paper-file your return so you can attach a statement that shows the settlement amount minus the (undeducted) medical expenses related to treatment.
To enter your 1099-MISC form, see Where do I enter an award from a taxable legal settlement?