In Gears of War 3 for the Xbox 360, there are quite a few executions you can unlock by getting a certain number of kills with the associated weapon.
Here is the list of executions you can unlock, and how many kills you need to get with the weapon in order to unlock its execution.
Boltok Pistol Execution – Get 40 kills with the Boltok Pistol
Boomshot Execution – Get 40 kills with the Boomshot
Cleaver Execution – Get 40 kills with the Cleaver
Digger Execution – Get 40 kills with the Digger
Gnasher Shotgun Execution – Get 200 kills with the Gnasher Shotgun
Gorgon Pistol Execution – Get 40 kills with the Gorgon Pistol
Hammer of Dawn Execution – Get 40 kills with the Hammer Of Dawn
Hammerburst Execution – Get 200 kills with the Hammerburst
Lancer Rifle Execution – Get 200 kills with the Lancer Rifle
Longshot Execution – Get 40 kills with the Longshot
Mortar Execution – Get 40 kills with the Mortar
Mulcher Execution – Get 40 kills with the Mulcher
Oneshot Execution – Get 40 kills with the Oneshot
Retro Lancer Execution – Get 200 kills with the Retro Lancer
Sawed-off Shotgun Execution – Get 200 kills with the Sawed-off Shotgun
Scorcher Execution – Get 40 kills with the Scorcher
Torque Bow Execution – Get 40 kills with the Torque Bow