Padfoot's Breed
Rowling never specified what breed of dog Sirius' Animagus form was, and 'a bear-like black dog' doesn't do much to narrow the field of possibilities. However, if we assume that the transformation closely reflects the wizard's personality, and perhaps reinforces it, I think I might have identified our mystery breed.
Meet the Russian Newfoundland, also called the Moscow Water Dog:
http://www.easypetmd.com/doginfo/moscow-water-dog
The result of a breeding experiment crossing Newfoundlands, East European Shepherds, and Caucasian Shepherds to create an all-purpose work and rescue dog by the Soviet Army during the 1950's, the Russian Newfoundland is now extinct.
What was this breed like while extant?
"This new breed proved to be an excellent swimmer, as well as a vigilant, trainable and intelligent shoreline sentry dog, and well able to withstand arctic temperatures and freezing water."
Strong swimming skills and high tolerance of freezing water - escaped from Azkaban by swimming the North Sea.
Intelligent - his teachers acknowledged him as bright, however much trouble he caused. The Marauders' Map is nothing to laugh at either.
Vigilant - before he was addled by Dementors he was certainly more attentive than James during their assault on Snape.
Trainable - this is the crux, isn't it? We don't know much about the dynamics between Sirius and James, but Peter was able to play him like a harp, and even Remus could control him when he bothered to exert himself. So, it seems that he was eminently manageable by those who knew him well and who he considered 'pack.'
And the Moscow Water Dog was infamous for being very selective about who they would acknowledge as pack, and how hostile they were toward strangers.
How hostile?
"...when set loose to rescue a panicked and drowning sailor, it was the breed's nature to swim straight to them and attack them in the water. A terrifying experience for the victim, who if they did not drown fighting off the dog would then likely try and drown the dog in order to defend themselves from the onslaught of gnashing teeth."
I'm sure those Muggle policemen in the prequel could sympathize deeply. As could Snape, and Kreacher, and....
In summation:
"As it would turn out, the Russian Water Dog was too much working dog and not enough rescue dog, the breed was aggressive and took very poorly to strangers, regardless of whether they were drowning or on land."
Yes, I believe that fits Sirius rather well.