(EDIT 10/12/2014 – My guess is the Nostalgia Critic’s “Boomer Will Live” might have already replaced this trope before I came up with it.)
The world may be coming to an end, evil runs rampant, corruption controls the government, and aliens are atomizing our cities and feasting on the brains of our youth, with tartar sauce, no less…
But that’s ok! Because the dog is safe!
This trope is somewhat of its own deal and somewhat the opposite of the “Kick the Dog” trope. Similar to how a “Kick the Dog” moment is where the author is telling the audience they’re free to unleash their unbridled hatred toward the bad guy, a “Save the Dog” trope is considered reason to root for our heroes when we have little other reason to not treat them with indifference. Occasionally, it can also be a moment to differentiate the “real” bad guys from the “sorta, not-really” bad guys.
It also doesn’t have to be a physical dog being saved. Any act of compassion or altruism that makes the audience go “aww” that seems to arise out of nowhere can qualify. However, the dog itself usually symbolizes “pure innocence”, and is assigned a higher moral priority usually subconsciously by the audience. The assumption is that while people may go on to commit evil, a dog is perfectly good and noble, making killing one like “shooting a mockingbird”.
In “Independence Day”, when Jasmine, in her desperate attempt to shield herself and her son from an incoming firestorm, pauses long enough to call her pet dog to safety…as opposed to all of the other people fleeing for their lives.
In “Godzilla, Mothra and King Ghidorah: Giant Monsters All Out Attack!”, Mothra appears to be just another rampaging kaiju when she kills a bunch of drunken late-night beachgoers. However, the news report the next day clearly shows that the dog the beachgoers were tormenting is perfectly safe…indicating Mothra is a “nice kaiju” because she punishes people who are cruel to animals.
At the start of the Baroque Works arc in “One Piece”, all exposure the audience has had previously with the Navy has been largely negative, revealing it to be filled with corruption. Captain Smoker is intruduced as a gruff, stern, no-nonsense officer of the Navy, but when a random kid accidently knocks into him and dumps his ice cream cone, Smoker’s only response is to give the kid enough money to buy a larger one, clearly telling the audience he’s “one of the good Navy guys”. This would be an example where the “dog” is an act of altruism rather than saving an animal’s life.
In “Dragonball Z”, the ultimate sign that Fat Buu is not “truly evil”, and what signals his moral turnaround, is when he pairs up with a puppy. He actually has another moment earlier which is one with an act of altruism (sort of…) rather than saving an animal in which he gives a formerly blind child (who he healed) a carton of milk…although he killed someone else to get it.
Also in “Dragonball Z”, the fact that Android #16 frequently cares for birds and small animals with a contented smile on his face is the big signal that’s he’s not as destructive or sadistic as the other androids. Again, an act of compassion as opposed to actually saving an animal, although he does that later too.
In “The Fly II”, the big signal that Martinfly has not degenerated into a psychotic mutant as Brundlefly did is when an attack dog is sent after him, rather than kill it, the monster simply pets it on the head.
In “Hellboy”, one of many signs that Hellboy is only a terrible demon “on the outside” is how he goes out of his way in a life-or-death struggle to save cats. Note this is an incidence where the “dog” is not actually a dog.
Another “cat” one is in “Alien”. In spite of the bloodthirsty monster killing crew members left and right (or worse, if you see the “Director’s” Cut), the audience receives extra incentive to root for Ripley to get out alive when she devotes enough time in her escape plan toward saving the ship’s cat.
In the original movie version of “The Amityville Horror”, the signal that George is “no longer crazy” is when he goes back into the demon-infested house to rescue the family dog.
The movie “The Birds” has an ambiguous one when Mitch goes back into the house to get the lovebirds. At this point, the movie had caused us pretty much to focus on Melanie and the Brenners over everything else, and there was no indication that the “wild birds” might have done harm to the lovebirds if they were left behind. However, they would have most likely inevitably starved to death if left alone in the cage. Again, this would be another one where the “dog” is not a dog.