Crucifixion is a form of punishment used by Caesar's Legion. The victim is tied to a cross and left out to die. Caesar chooses to do this because the punishment was frequently used by the real Roman Empire. It was public, humiliating, and lingering, as well as being cheap and easily arranged (many of the crosses Caesar's Legion uses are recycled power or telephone poles).
Caesar's Legion appears to use only the form of crucifixion in which the victim is tied to the cross, not that in which the victim is nailed. Although nailing a victim appears to be a harsher treatment, it is in fact more merciful, since the victim will die much more quickly with the assistance of shock and loss of blood. In Roman times, tied victims would often last several days, during which time they might have to endure having their eyes or cheeks ripped out and eaten by vultures, crows, and other birds.
Crucified Powder Gangers can be found in Nipton, along the side of the main road running towards the Nipton Town hall. Crucified slaves can be found just off the road to Cottonwood Cove. Captured NCR troopers can be found crucified at Nelson. Disobedient legion soldiers, NCR soldiers and raiders can be found at many Legion settlements such as Cottonwood Cove and The Fort.
The Courier can put crucified people out of their misery for no Karma loss. These "kills" do not give XP, even if the crucified person is a member of an enemy faction such as the Powder Gangers, but they do count toward kill total and progress toward such perks as Lord Death. The only thing that can be scavenged from the corpses is their clothing (Caesar's Legion does not follow the Roman practice of crucifying victims naked).
With a few exceptions, such as the three crucified NCR soldiers in Nelson and the Great Khan drug runner Anders at Cottonwood Cove, crucified victims cannot be set free alive (Anders can only be freed as part of a quest). Benny can also be crucified if the Courier chooses after they go into the bunker underneath Fortification Hill for Caesar. This seems to be the only way of killing Benny that actually frightens him. This also makes it impossible to get Benny's unique pistol Maria unless it is pick-pocketed before ordering his death.