It depends. It depends on what supplements you mean, and what person. Probably everyone needs a good basic multivitamin to support ongoing good nutrition. Many of us are also exposed to environmental toxins, so that extra antioxidants (if the right kind!) can be protective. Some people need replenishment for specific nutritional deficiencies -- there are many different types. There's no 1 size fits all.
Not everybody. People need dietary supplements (vitamins, minerals, micronutrients) if their diet is poor or limited. Or if they are unable to absorb them from their diet. Excessive supplement use can be dangerous. E.G., vitamin a overuse can lead to significant brain and liver toxicity. It's best to discuss your nutrition with your doctor.