Final answer:
The axillary nerve is the most commonly injured nerve in anterior shoulder dislocations due to its location near the surgical neck of the humerus and its proximity to the dislocation site.
Step-by-step explanation:
Shoulder dislocations often occur in scenarios such as sports activities where a force is applied to the upper limb when fully abducted. Anterior shoulder dislocations can lead to injuries to nerves that innervate shoulder and upper limb muscles. Among these, the axillary nerve is the most commonly injured nerve during an anterior shoulder dislocation due to its proximity and the mechanism of injury involved. This nerve passes through the quadrangular space and wraps around the surgical neck of the humerus, making it susceptible to injury when the humeral head is dislocated anteriorly.