I'd stop without hesitation. Sure, as the driver you can go ahead and say that the owners are at fault for not having him on a leash... but that doesn't change the fact that you hit the animal. In my eyes, whether it was 10 or 50 mph, the driver should at least take on the simple responsibility of checking to see if the dog is OK. The last thing I would want on my conscience is the idea of me not stopping to check on a dog that probably could've been saved.

My last dog was a bull terrier that I grew up with and had for 15 years. She died of natural causes, but if she had been hit by a car and the driver actually stopped, I wouldn't be pointing the finger or "getting into it" with the driver; a scenario that some of you have suggested would happen. At that point, I'd be more concerned about whether the the dog could be helped, as opposed to placing blame on someone and getting into pointless fights about who is at fault.