Baseball injuries tend to usually centre around the shoulder and elbow, due to the high forces involved. This is especially true in pitchers, but other positions, as well as batters may also suffer with this kind of injury.
Medial ligament injuries at the elbow are the most common injuries in pitchers. This is damage to the ligament on the inside of the elbow, caused by repeated stress. Golfer's elbow is another injury which is common and is sometimes actually called throwers elbow. It is a degenerative condition of the tendons of the forearm muscles where they attach to the inner elbow.
Here are the six most common baseball injuries. We also have an article on how to prevent injuries in baseball on the training and advice tab.