Of all the characters to kill off, Punisher, in a one-shot comic book called 'Punisher Kills the Marvel Universe', manages to finish off Wolverine.
The wiki article is vague; how does Punisher kill off Wolverine?
The Punisher blew up all of the other X-Men and most of the major X-Men villains in a giant nuclear explosion on the moon. He then attacked Wolverine whilst he was drunk from drowning his sorrows after losing most of his friends. During their fight he stabbed Wolverine in the throat with a knife and in the chest with Wolverine's own claws and threw him into an electrical generator. Wolverine's claws pierced the generator and Wolverine was electrocuted until he basically melted down to just his skeleton.
In some stories that wouldn't be enough to kill him. In some it is. This is obviously the latter.
He throws Wolverine into some sort of "Maximum Voltage" panel ...
... which electrocutes him: