A lot depends on the individual dog, its age, past experiences, etc. I had a Siamese cat when I brought my dog home as a puppy. She was top cat and remained there until she passed away last year at 16 years old. As a result, this year when I brought home a 1 year old cat, my 12 year old dog has acted wonderfully with her, even though she is challenging to say the least! (She often charges him playfully, while he pretends she is not there; then when he walks past her, she bats his tail).
My German Shepherd knew that the litter of kittens we had belonged and never at any time tried to hurt them or the two other cats we had at the time. My Malamute, on the other hand, I never trusted to be around any of the cats without close supervision.