The answer depends on several factors such as the specific sport, position played, and acute versus chronic injuries.
In terms of acute injuries, sprains (stretching/tearing of a ligament) are extremely common in sports. Sprains of the ankle are common and can be managed conservatively in most cases. A common mistake we see is overlooking an appropriate rehabilitation program. We often see recurrent sprains and ankle laxity in those athletes not undergoing rehabilitation.
In terms of chronic/overuse injuries we often see patellofemoral pain syndrome. This condition can often be secondary to training errors and/or muscular imbalances around the lower extremity.