Ace was a German Shepherd originally owned by an engraver named John Wilker. He was found by Batman and Robin after his master was kidnapped by a gang of counterfeiters. Batman used Ace to try to locate Wilker. Because he had already placed a large number of "lost dog" announcements for Ace in his civilian identity of Bruce Wayne, he was concerned that anyone recognizing Ace (who had a prominent star-shaped marking on his forehead) might make the connection between Bruce Wayne and Batman. To forestall that problem, he hastily improvised a hood-like mask for the dog that incorporated the bat emblem as a dog tag dangling from Ace's collar. Ace was subsequently christened "The Bat-Hound" by a criminal he helped Batman to apprehend.
Wilker later took a new job that made it difficult for him to take care of Ace, so he left the dog to Bruce Wayne. Wilker was never aware that Ace was the Bat-Hound or that Bruce Wayne was Batman.
At one point, Ace acquired super-powers thanks to Bat-Mite but this was short-lived. He did have his own training. For example; his specialized radio collar, when activated told him to don his own mask (via a hands-free device) and track down Batman and Robin.
Ace disappeared from the Batman comics after Julius Schwartz took over as editor in 1964, and made only very occasional comic book appearances in the years afterward.
A version of Ace is seen in the cosmic realm Limbo when the hero Animal Man takes a trip through it.
A modern-day version of Ace was reintroduced in Batman #462 (June 1991), although he has been rarely seen in recent years. This version was originally a guide dog belonging to a blind Native American named Black Wolf, who called him "Dog". The dog assisted Batman in fighting criminals from Black Wolf's tribe. Following Black Wolf's death, Batman adopted Dog, renaming him Ace.
He did not wear a mask, nor was he ever referred to as Bat-Hound, and has the appearance of a beagle-pug crossbreed (which exists in the real world as a puggle) with a bat-shaped dark patch on his flank. Ace has at times helped Batman on cases  and is depicted to be very affectionate towards his owner and vice-versa.
After Batman is disabled by the villain Bane, Azrael takes over the role and ejects Ace, Nightwing, Robin and Harold Allnut from the Batcaves. Harold, a trusted confidante of Batman, takes in Ace; they live in a part of the caverns Azrael is unfamiliar with. To keep busy, Ace enjoys playing with a robotic mouse built by Harold.
A traditional Ace was seen in Final Crisis: Superman Beyond 3D. He is in limbo with other "forgotten characters", such as Gunfire, Geist, Hardhat of the Demolition Team and Merry Man of the Inferior Five. Merry Man explains everyone is here where no stories exist because nobody is writing about them. Despite this, Superman and his allies work to rescue all the residents of Limbo, who then help assist in the battle against the cosmic threat of Mandrakk.
The original Ace appeared in a flashback scene in Batman Inc. #4, thus making the current canon status of the Post-Crisis Ace unclear. In this story, Ace is trying to play with Robin who is fuming over Kathy Kane, Batwoman, and her influence on Batman. 
The New 52
In Batman and Robin Vol 1: Born to Kill, Bruce is seen purchasing a black Great Dane from a kennel. He later gives this dog to his son Damian who names him Titus, though writer Peter Tomasi stated in an interview that he considered naming the dog Ace.
Ace appeared in the late 1990s animated seriesBatman Beyond, with vocal effects done by Frank Welker. This version is Bruce Wayne's pet/guard dog that's a Great Dane mix. He made his first appearance the series premiere episode "Rebirth" as a fiercely loyal pet to his aged master. At first, Ace did not like Terry McGinnis. But after he and Terry were able to help each other on several missions, Terry earned Ace's affection and loyalty. In the episode "Splicers", Terry briefly reflecting that Ace's loyalty was one of the 'small rewards' that he had gains as Batman. The episode "Ace in the Hole" reveals Ace's origins: he was a puppy that was bought by illegal dog-fighting ring leader Ronnie Boxer but managed to escape this abusive, violent life. He soon found Wayne (a fellow tormented soul) at Crime Alley during the anniversary of his parents' murders. After he was injured by one of the Jokerz during an attempt to save Bruce from the thug, Bruce took the dog to a veterinary hospital. Since there was no one to claim Ace and both the elder man and the dog desired companionship, Wayne took him in as his owner. After encountering Boxer once again, Ace and McGinnis stop Boxer's attempt to use synthetic growth hormones to turn dogs into monsters. Ace also plays a role in the movie Batman Beyond: Return of the Joker when he engaged a member of the Jokerz who had been spliced with hyena DNA and then attacked the Joker which damaged the controls for Joker's new satellite weapon system and freed Batman (Terry McGinnis) from captivity. Ace has also been alluded during the movie Batman: Mystery of the Batwoman when Robin (Tim Drake) commented that a dog could help "sniff out clues" and during the Justice League Unlimited episode "Epilogue" suggested that the dog might be named after the Ace from an early incarnation of the Royal Flush Gang that Batman (Bruce Wayne) briefly befriended before her death.
Ace in the 2005 cartoon series Krypto the Superdog.
In the 2005 Cartoon Network animated series Krypto the Superdog that stars Krypto (Superman's childhood dog), Ace the Bat-Hound (voiced by Scott McNeil) makes occasional appearances and is once again a crimefighting ally of Batman—although the Dark Knight himself does not appear on the show. In this series, Ace, much like Batman, is equipped with various gadgets and equipment as an aid in his crime-fighting efforts. In one episode, he met the Dog Star Patrol and helped them find their missing member Hot Dog. His enemies include the Joker's hyenasBud and Lou, the Penguin's trained birds (Artie the Puffin, Griff the Vulture, and Waddles the Penguin), and Catwoman's pet cat Isis (who flirts with Ace much like Catwoman flirts with Batman). Ace has a Batwoman-style glider he uses for more speed. He considers himself to be Batman's partner, rather than his pet.
Ace the BatHound was alluded in The Batman animated series when Alfred Pennyworth remarks "Perhaps I should equip the Batcave with a doggie door, should Bat-Hound decide to join the gang." during Batgirl's introduction.
Ace the Bat-Hound appears in Batman: The Brave and the Bold, with vocal effects done by Dee Bradley Baker. In the episode "Legends of the Dark Mite!", he helps Batman fight Catman and an endangered tiger he unleashes on Batman. Ace manages to corner Catman up a tree, and Batman rewards him with a bat shaped treat after getting him to heel. Ace is later seen in the episode's main plot as a guise Bat-Mite created. When Batman see two Aces, he knows something is wrong. At the end, Batman touches Ace's collar to see if he is a fake, but he's the real thing and tells Ace that he was just making sure. Ace makes an appearance in the episode "The Siege of Starro! Part One" where he is seen when Batman contacts Booster Gold. In "The Plague of the Prototypes!", Ace is friends with Batman's prototype Bat-Robot, Proto, and encourages him to save Batman from Black Mask. Later, using his jet-pack, he helps Batman and Proto track down and deactivate Black Mask's bombs.
The appeal of Ace is discussed in 'Mythology: The DC Comics Art Of Alex Ross'. Ross feels that as a child, the idea of Batman having a dog is 'cool' but as an adult the same idea is 'outrageous'. Art from Ross and 'Batman: Annual 1 (1961)' is showcased. 
^Irvine, Alex; Dolan, Hannah, ed. (2010). "1950s". DC Comics Year By Year A Visual Chronicle. Dorling Kindersley. p. 77. ISBN978-0-7566-6742-9. "Once Superman had a dog, Batman got one too, in "Ace, the Bat-Hound!" In the story by writer Bill Finger and artist Sheldon Moldoff, Batman and Robin found a German Shepherd called Ace."
^Shutt, Craig (1994). Baby Boomer Comics: The Wild, Wacky, Wonderful Comic Books of the 1960s!. Krause Publications. p. 98. ISBN0-87349-668-X.