The Kill-o-Zap is a weapon first appearing in the novel The Hitchhiker's Guide to the Galaxy, wielded by the police from Blagulon Kappa when they come to Magrathea to arrest Zaphod. It is referenced throughout the series in the role of a standard and widespread brand of raygun.
In the novel The Restaurant at the End of the Universe it is described in more detail:
"The designer of the gun had clearly not been instructed to beat about the bush. 'Make it evil,' he'd been told. 'Make it totally clear that this gun has a right end and a wrong end. Make it totally clear to anyone standing at the wrong end that things are going badly for them. If that means sticking all sort of spikes and prongs and blackened bits all over it, then so be it. This is not a gun for hanging over the fireplace or sticking in the umbrella stand, it is a gun for going out and making people miserable with.'"
In the novel Life, the Universe and Everything, the group arms themselves with Kill-o-Zap guns against the Krikkiters. Arthur Dent "fumbled to release the safety catch and engage the extreme danger catch as Ford had shown him. He was shaking so much that if he'd fired at anybody at that moment he probably would have burnt his signature on them."
In the 2005 movie adaptation, the gun has a sophisticated look. It is more of a white sphere that covers the hand and has a trigger on the inside. This version is wielded by Marvin.
Presumably, the name is meant to evoke the 'overkill' of the destructive potential of the weapon.