What are the most common sports injuries?
The most common sports injuries involve the knee, shoulder and elbow joints.
Approximately 55% of athletic injuries occur in the knee. The shoulder is the next most frequently injured joint in sports; approximately 20% of sports injuries. The elbow is the third most frequently injured joint; approximately 7% of sports injuries.

How are sports injuries treated?
Most often sports injuries can be treated without surgery with the application of several general treatment principles:

1. Rest
   Avoid the irritating activity or sport until you can go through your normal daily routine (usually less vigorous than sports) without pain or difficulty. This may be only several days; it may require several weeks or even months for more severe injuries.

2. Ice
   Ice helps for 10-20 minute periods several times a day for 2-3 days after the injury. Ice slows the blood flow at the place of injury and thereby decreases swelling; it also has mild analgesic effects which help diminish pain.

3. Medication
   Non-steroidal anti-inflammatory medications (such as Motrin or Advil) help to decrease inflammation, and thereby pain and swelling, at the injury site.

4. Maintain endurance
   While you are resting your injury, you should maintain your endurance by cross training. This includes choosing another form of exercise which does not stress the injured area (i.e. stationary cycling after an elbow injury.)

5. Rehabilitation
   Once there is no pain at the injury site, then you can begin to move the injured area. This is done by slowly increasing its movement to match that of your other uninjured joint or muscle. Once full motion (compared to the other side) is achieved, then you may begin to strengthen the area. Light weights can be used and slowly increased until the strength of the other side is matched.

6. When to call the doctor
   Some injuries are more serious and should be seen by a physician as soon as possible. These injuries cause obvious deformity, inability to move a limb or joint, numbness in an extremity or severe pain at the place of injury.

You can carry out these six simple treatments yourself. Often they will allow athletes to return to their sports safely and quickly. Sometimes the injury continues despite these treatments and you should see a doctor. Your physician may choose other non-surgical treatment (i.e. prescription non-steroidal anti-inflammatory medications or formal physical therapy.) Sometimes however surgery, often arthroscopic, is necessary to return to sport.

Here is an interesting paper on: 
An epidemiologic investigation of injuries affecting young competitive female gymnasts  (leaves US Gyms.Net)