Who's a good boy then? ACE THE BAT-HOUND
In early 1955, Krypto the Super-Dog debuted in a Superboy story. Just as there had to be a Bat-Mite as a counterpart to Superman's Mr Mxyzptlk, Batman figured now he had to have a dog too*. There was a bit of meta-competition between the two heroes building their "Families." (Well, actually it was the editors desperately looking for ideas to fill all those pages every month.) I'm a little surprised Green Arrow didn't immediately get an Arrow-Dog to match his Arrow-Cave, Arrowplane, Arrow Signal, Arrowmobile, boy sidekick or counterpart (Speedy/Robin/Superboy in a way) and girl counterpart (Miss Arrowette/Supergirl/Batwoman-Batgirl). Real herd mentality in those days. Aquaman did the same thing with the kid sidekick and Aqua-Cave and Quisp as his Bat-Mite, his "dog" would be the octopus Topo.
So, in BATMAN# 92, July 1955, Bat-hound made the scene. He was created by Bill Finger (as Bob Kane would say, "who?") and Sheldon Moldoff (Kane referred to all the artists as his "ghosts").
Anyway, Batman didn't actually set out to acquire a dog. As Bruce Wayne, he put notices in the newspapers about a stray German Shepherd he had found. It turned out the dog's owner had been kidnapped. Then, as he and Robin set out to rescue the man, Ace jumped into the Batmobile to go with them. Too late to turn back. Since Ace had a distinctive mark on his forehead, there might be a problem if he was seen in the company of both Batman and Bruce Wayne, so Robin fashioned a black mask for the dog and hung a little bat emblem off his collar. Why not? You could say that, like so many others, Ace adopted a secret identity to protect his loved ones (ha ha).
Although Ace was returned to his owner, eventually Wayne ended up with custody of the dog. This 1955 Batman was much more normal and well-balanced emotionally than today's version. He started training Ace as a helper. This in itself is not so far-fetched, after all German Shepherds have an admirable record in helping police, armed forces and rescue work. But, DC being what it was, Ace developed skills a LITTLE too advanced for a dog. He also started have thought balloons with complete sentences (this was okay for Krypto and Streaky, they had super-powers and their intelligence was boosted). I remember one story where Ace acquired Kryptonian super-powers but then, in the Silver Age everyone from Perry White to Lady Blackhawk to Sugar and Spike acquired super-powers once or twice.
One trick I loved was that the mask was held up on a frame so that Ace could slip into it when necessary, having no hands after all.
Ace was around for years, sometimes more in the spotlight than other times but eventually only doing background cameos. I figure he was getting old and arthritic, being a dog after all. In 1964, Julius Schwartz was called in to revamp the Batman series. He emphasized detective work over fighting bizarre aliens, the yellow oval around the chest symbol was introduced, and most of the Batman entourage was quietly sent to Comic Book Valhalla. Ace went with them.
Since then, I gather writers have sometimes introduced a new dog in Batman's life, but they haven't worked out or shown any staying power. It's too bad, I think having a dog would do today's Batman a lot of good. Comfort dogs (like those golden retrievers brought to the children at Sandy Hook) are used to help heal trauma victims who have suffered more than he has.
Also, I should mention there was a real "Ace the Wonder Dog," who appeared in movies from 1938 to 1946 (a better career than many human actors!). I've only seen him in the pretty-good Columbia serial THE PHANTOM with Tom Tyler. Ace plays Devil, the Ghost Who Walk's wolf, and he has immense charm and steals one scene after another. This is why actors advise against appearing with babies and animals.
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*But this opens a metaphysical headache. The Superboy stories took place ten or fifteen years in the past, so whatever was introduced in them was now something that had always been there. Even though Krypto had never been seen before, suddenly he was part of Superman's history and always had been. This must have driven the Superboy writers nuts, since anything they did could not be allowed to alter the more important Superman continuity without a lot of consideration. It's 1984 all over again ("We have always been at war with Eastasia... no, we have never been at war with Eastasia.")