From comic books nerds who know what they are talking about:

"Laid out in the Xavier Protocols, which I believe is where this started, was that he had to be decapitated as well his head kept from his body so he wouldn't mend together. So like Deadpool the keeping his head away is key. Likewise how it was shown in AoA that he couldn't have an arm as it was apparently not around to mend, and can't seem to regrow his own skeleton, hence the adamantium protection, and Laura reattaching her own limbs. (silly aside from the biology of this being comical of course, that in AoA no one could make him a prosthetic, given how commonplace they are in MARVEL and AoA even?). To my knowledge this has never happened in 616. He has been killed in alternate Universes. A case in point was in What If? Hulk Killed Wolverine where Hulk punched part of his spine out close to his neck and Wolverine died. As well, What If? Enemy Of The State where Kitty phases and fuses her own arm to his head and brain killing him. Again alternate timelines and anyone's reluctant to apply those to CANON, odd in a way to me as they are meant to show specifically what would happen in canon where a different factor in play or incidents played out differently then they had in the first place. Likewise though the fate of Sabretooth in 616 could just as well be applied here for arguments sakes really since we're talking about the same power, sans adamantium."

But you can't base it off Deadpool's. This is why: "The mercenary Deadpool is depicted having a humorous exchange with the entity in a self-titled Annual. Deadpool becomes infatuated with Death after he has a number of near-death experiences. During the Funeral for a Freak storyline, Death appears to reciprocate the feeling, and a jealous Thanos prevents Deadpool from dying and joining the entity and curses him with immortality"

In other words, Deadpool's is a cheat, and Wolverine can die via massive damage to the spinal column/decapitation. But even this doesn't sit well with me, mostly because if you can't die, what's the point of any of us in a fight? We would just send Light in and no matter what, she would win. Our only usefulness would be if she was captured. Even if she was a lousy fighter, she would still outlast the enemy, and would kill them after they have exhausted themselves. And with such a powerful healing factor, comes living longer, and then you hit a Groundhog's Day/Ben 10's Paradox scenario. Boredom. She'd get so damn bored, she'd learn. And learn. And learn. And learn. And learn. Hell, she'd be more powerful than anyone in the One Piece verse. She'd basically be a goddess. That's why I can't stand villains who want immortality. They never seem to understand the sheer boredom it would bring.