Wolverine isn't a simple character. One moment he may love his friends, the next he may hate them. He saves the day only slightly more than he finds ways to ruin it. He has layers, like an onion. He plays the part of hero, but he's also scarred by unspeakable tragedy and the image of Wolverine murdering innocent people isn't exactly rare. Wolverine will almost certainly never find happiness.
Does Wolverine kill innocent people? You can't spend as much time killing as Wolverine does and not. Just review the Wolverine backstory and you'll find plenty of times when he hurts innocents, including many times when he did so reluctantly. A lot of the innocent people Wolverine has killed over the years have been out of necessity, out of mercy, or for the greater good. Wolverine's ability to make those tough decisions is another reason why we can't get enough of him.
Read more to see examples of Wolverine murdering innocent people, and as you learn more about his back story, maybe you'll even wonder which side he's really on.
Ask any major Wolverine fan what their favorite comic storyline is, and most of them will probably say Old Man Logan. It was a comic series that took place in an alternate future where a hodgepodge of super villains ran the world. Where were all the heroes to stop them? It turns out most of them died at the hands of Wolverine. That's right, he kills most of the world's heroes. Flashbacks throughout the story show a group of enemies invaded Xavier's school and Wolverine killed them all, brutally, in order to to protect the mutant children. In a tragic twist, it turns out that it was all an illusion set up by Mysterio and Wolverine murdered nearly all of the X-Men.
Wolverine lives a tough life. Sure he has those awesome claws and that life-extending healing factor, but still. Tragedy and death follow him everywhere. Remember the time Wolverine killed the woman he loved in Wolverine Vol 2 #57. Mariko Yashida was the daughter of a Yakuza crime boss in Japan and the two fell in love and got engaged. When an assassin named Reiko poisons her with deadly blowfish toxins, she asks Wolverine to help her avoid a painful, drawn-out death. He grants her final wish.see more on Mariko Yashida
It's proven time and time again that Wolverine will do anything necessary to save others. In Ultimate X-Men #41, a teenager starts gaining his mutant powers for the first time, and just like for so many of the X-Men before him, it's a little weird. There's just one problem: he has the ability to produce a toxic secretion from his body that burns everyone around him - to death. He can't control the power and 265 people die as a result. Wolverine's healing power makes him the only one who can get close to the kid. Which he does. They share a beer together, then Logan mercifully kills the teenager to protect everyone else.
Wolverine definitely has a problem with killing the women he loves. One of his very first kills was that of Rose O'Hara, Wolverine's childhood friend and the first person who accepted him for who he was. They frequently traveled together as children, and on one trip O'Hara fell in love with somebody else. Good-guy Wolverine was eventually just happy that she was happy. But in Origins #6, things got messy when one of Wolverine's enemies, Dog, arrived to seek revenge. Wolverine engages Dog in the street and is closing in on the kill when Rose intervenes to stop him. Wolverine accidentally stabs and kills Rose instead, causing him to isolate himself in the wilderness for a good long while.