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.