This is a potentially contentious issue. Personally, I advocate and practice natural horsemanship. What is in the best interests of the horse.
Hammering nails through a horse's hooves is not usually ideal for a horse. It puts holes in the hoof, there is the potential for injury, plus the shoes are hard and slippery. The metal slamming against hard surfaces removes the natural flexibility of the hoof to cushion each step. On concrete or roads they can be slippery.
If there's issue with the hoof and riding, it is better to address the source of the problem, which is often nutritional or can be related to poor trimming. Healthy hoof growth relies on a balanced nutritional diet, so all trace elements and requirements such as biotin are met. It is also important that horses have a dry place to stand during wet weather. Standing in bog or mud constantly can cause the hoof to become infected.
The other issue which can be related to nutrition (founder) or mechanical (poor hoof trimming, poor shoeing, relentless riding, is laminitis. Some people advocate showing the help adjust the angle the hoof sits.
If there's a lot of riding and it is taking its toll on the hooves, boots are a less invasive option than shoeing and can be removed after the ride.