killing wolverine sans adamantium, according to the xavier protocols:
sever his head from his body and keep it a safe distance away until the body dies. no chance of the nervous system surviving to keep him moving, no chance of his tissue merging back together post-mortem and "regenerating" him.
killing wolverine avec adamantium, according to the Days of Future Past:
get a sentinel to do it for you.
killing ultimate wolverine avec adamantium, according to Gambit:
piss him off at a carnival, charge his skeleton, blow him apart. [and it's unknown whether or not 616 gambit can charge adamantium, though there's no real logic against it happening, there are typically differences between ultimate powers and 616 powers...]