The more I watch cat-dog interactions, the more I feel that cats vs dogs is just a myth created by media and literature for content. Never saw dogs aggressively behaving against cats, or cats bothering dogs. If I found a dog barking at a cat, it was more likely that it was the type which would bark at anything that moved.
I own multiple dogs and cats, and they've never been anything but friendly to each other.
AFAIK the is more probable if at least one of them met the other species while being young. Ideal case: both individuals met while being newborns.
I myself have a Japanese Akita and a long hair Munchkin, they get along really well. Many friends of mine also have both dogs and cats in their home, they don't fight each other at all and can be really intimate sometimes.