Wolverine vs. a pitbull trained to fight in those illegal dog fights.
I had read that a trained pitbull could take a wolf on the account of the pitbull's ruthlessness. The pit would viciously and suddenly attack; and the wolf, even thought it is wild, would hesitate enough that it would be at the disadvantage. Wolves, I guess, are not mean enough. Just instinctual. Wolverines, on the other hand, are mean as cat's piss, and will drive off larger predators just out of sheer ferocity.
Might make an interesting series - before Weapon X tried the bonding procedure on Wolverine, it experimented on animals, as well as the method used to give Deadpool his healing factor (the differences between a dog's metabolism and a human's meant the dogs looked normal whereas Deadpool looked like ... Deadpool)
One of the researchers took one of these dogs, a pitbull, home with him, hoping to extract the healing factor to sell to a medical corporation. However, the feral animal tore him and the house apart (the dog has adamantium bones and teeth), only stopping to spare the neighbour boy who fed it.
The dog is as long lived as Wolverine, surviving as the boy grew up, living alone, going out late at night for walks. Sometimes he hears of something that needs attention - his and his dog's.
On topic - the dog might take a few chunks out of him, but Logan'd probably win. Four or five, the same result. Wasn't there an issue where he intimidated a pack of wild dogs just by growling at them?
There are clips of a single Wolverine driving off 3 wolves.
http://youtube.com/watch?v=7VoKioxH-5Q I found one clip of a wolverine driving off 2 wolves, but there is another clip where a wolf and wolverine fought and the wolf couldn't hurt the wolverine even when it bit into the skin because the skin was so loose.
The same could be said for badgers. The wolf bit into the wolverines neck from behind and the wolverine could just turn around and slash at the wolfs face. After a while the wolf took off bleeding, but the wolverine was fine and went running back to its food.