Cheshire the Cat said:
Fire a few rounds into his eyes. Scrambles his brain. Sabretooth has a way better healing factor than Wolvy and it took him months to recover from a claw to the brain. So ya, shoot him in the eye socket then when hes down cut his head off. The bones may be adamantium but the ligaments are not.
Wolverine has survived being shot in the brain repeatedly. So too have others with his healing capacity. Both Wolverine and Cable have survived having their brains burst by Stryfe and Cable respectively.
Also, Sabretooth has been dead for years. Wolverine killed him.
There is no "has", and Wolverine's healing powers have become more potent since the days when a claw to the brain was a serious injury.
In the main Marvel continuity, Wolverine's body
cannot be ripped apart, despite any suggestion that his ligaments should not be able to take the strain. Even the Hulk has failed to rip his limbs off. It's only really in the Ultimate Universe that his body is susceptible to this damage without the adamantium being removed. Don't like it because it doesn't make sense? Tough, I guess, that's the canon for you.
Here's some more general stuff about Wolverine's survivability (for the most part, this is only about the mainstream version of Wolverine):
In the main comics continuity (Earth 616), the Muramasa blade slows Logan's healing factor, to the point where he can be killed. Wolverine himself used this blade to kill Sabretooth, while Wolverine's son has used the blade's metal to almost succeed in killing the Hulk's son.
Carbonadium greatly slows Wolverine's healing abilities when introduced into his system. Shoot him with enough Carbonadium bullets and he'll go down long enough to be butchered to death.
Wolverine's infamous regeneration from a skeleton in the main continuity (during Civil War) has since been explained as due to extenuating, supernatural circumstances. He can't regenerate from mere bones under his own steam. Therefore, you CAN burn him, dissolve him, etc and expect him to die. Simply put, if you take too much of his body from him at once, Wolverine, and people like him (X-23, Daken, Sabretooth, Deadpool - when Wade's not "Cursed with Life")
will die.
Removing Wolverine's head from his body for too long will also kill him. Granted, this is almost an impossible task due to the adamantium lacing his bones, which (somehow - as I said earlier) DOES PREVENT LIMBS AND EXTREMITIES FROM BEING RIPPED OFF in the main Marvel continuity (though it famously didn't stop the Hulk from ripping him in two in the
Ultimate Universe, in which Wolverine has different limitations and powers). While their healing factors may operate with different restrictions, Deadpool has also regularly faced death when his head was removed.
This was proven again recently, when Cyclops, Namor, and Magneto tried to kill Wolverine while a demon was possessing. Magneto held him still and removed enough adamantium from one of his neck vertebre for Namor to rip off his head, and then Cyclops blasted the remaining pieces into a crater. Well, this was the plan. The demon within Logan was capable of spewing hellfire though, which wasn't taken into account when Cyclops devised a strategy for killing normal ol' Logan.
When facing the Adamantium Men (a squad of artificial Wolverine knock-offs), Wolverine managed to kill the entire bunch using his wits and intrinsic knowledge of his own weaknesses. For instance, he attacked some with a helicopter gunship as they waited for him on an oil rig, then drowned them while they were weakened. Wolverine's internal monologue notes how he has more difficulty in water than he does on land, as the density of his bones prevents him from floating without conscious effort on his part. He can swim, but it's harder work for him than it would be without his adamantium, which allowed him to drown his weary knock-offs while they were exhausted and he was fresh. Also, the Adamantium Men tried to take Logan down using darts that would introduce dozens upon dozens of the world's deadliest diseases into his system simultaneously, overloading his healing factor and making him easy prey. Let's just say that he turned this guns on his knock-offs to great effect.
Cyclops recently planted a series of nanobots in Wolverine's system that turn off his healing factor remotely. Cyclops is somewhat becoming the Batman of the X-Men, with measures in place to deal with any of the X-Men if needs be. These particular bots were used to secretly strip Wolverine of his immunity to a vampire's bite, allowing enemy's of Blade to force Logan into their ranks, only for Cyclops to reactivate Logan's healing factor, purging the bite's effects, and leaving a very pissed off Logan within arm's reach of vampires who'd thought him their secret weapon. Needless to say, a lot of Edward Cullens died.
Magic can also fuck Wolverine up a treat. The demon Belasco reduced X-23 (Wolverine's female clone and adoptive daughter) into a pile of bones during an encounter she had with him. She didn't heal herself, only surviving because he kept resurrecting and killing her himself to be sadistic.
I could go on forever detailing how Wolverine could be killed/has been killed/has been put in mortal danger. It happens a lot. I won't though, because there's only so long I can type this stuff before it bores me.
The important thing to remember is that, despite the infamous image of him returning to life from a skeleton in seconds during Civil War, Logan can't self-resurrect and can't heal from virtually nothing with his powers alone.
Back to the OT's post: Some of these methods of killing him are applicable in the real world (drowning, burning, blowing up, throwing into space, etc), some are not (carbonadium, nanobots, magic, Muramasa blade).