Damage Multiplier

A damage multiplier is the number that the base damage of a weapon or attack is multiplied by to yield the actual damage. Although the values of the numbers have changed throughout the series, generally the head and neck increase damage, while hitting the limbs and hands will decrease damage.

Call of Duty and United Offensive
Call of Duty and its expansion pack United Offensive were unique in that its damage multipliers were shared by all weapons, while in later installments each damage multiplier was different for every weapon. The table below lists the damage multipliers from highest to lowest.

Call of Duty 4: Modern Warfare, Call of Duty: World at War, Call of Duty: Modern Warfare 2, Call of Duty: Black Ops, and Call of Duty: Modern Warfare 3
In these games, multipliers were the same for all classes except for snipers and shotguns.

Assault Rifles, Submachine Guns, Light Machine Guns and Handguns
All weapons have a 1.4 multiplier to the helmet and head, with the exception of the M14, which has a 1.5 multiplier to the helmet, head and neck.

Shotguns
Shotguns have no multipliers, so there will be no area on the body in which they will cause more damage.

Sniper Rifles
Snipers are unique as they have additional multipliers on the neck and torso rather than just the helmet and head. In Modern Warfare 2 and Black Ops, all snipers have a base damage of 70, unless silenced, in which it drops to 50.

Trivia

 * Any damage done to the limbs will have a 1.0 multiplier applied, the same as any other weapon, with the exception of the L96A1.
 * Besides sniper rifles, the MP9 and Skorpion in Modern Warfare 3 have the highest headshot multiplier in the game.