For realistic dogs in games, you could probably look into how Dogmeat, the dog from Fallout 4, was created. I'm not a 3D artist so I'm mostly guessing, but it looks like a finished dog model, fur and all, with only the trimmings around the neck and ears perhaps using alpha blended geometry. The rest I'd imagine is all done with normal maps and texturing.
I'm guessing you're avoiding using particle hair entirely? I thiiiink the longer haired dogs from the Sims 3 Pets use particle hair but I could be mistaken. Regardless it would serve as good reference anyway.
At a more indie level, you could try look into how the fur on the fox in Never Alone was made. Pretty sure it's just a full mesh though, with some sort of glow/blur trickery applied
If you're going for something more cartoony though, you could do away with fur entirely, ala Paw Patrol style.