The Dog Is an Alien

Some sort of alien lifeform comes to Earth, and, to avoid attention from The Men in Black, disguises itself as a domestic animal, usually a dog. Sometimes the alien happens to already look like a dog, while others may transform themselves using Voluntary Shapeshifting or Applied Phlebotinum.

The latter variant raises some questions as to why the alien wouldn't choose to disguise itself as a human, giving itself far more freedom within human society. However, given that their disguise may not be perfect, or that they may be unfamiliar with human social norms, this may be a sensible decision. A dog that acts or looks a little bit odd is less likely to attract attention than a human who acts strangely or looks creepy.

The alien often finds itself adopted as a pet, usually at least somewhat willingly. After all, a family who is willing to provide food and shelter seems like a reasonable alternative to living on the streets avoiding The Men in Black and dog catchers, and the alien probably reasons that it is capable of escaping if it needs to.

This trope comes in both benign and malevolent variants. The former tends to result in A Boy and His X.

The most common variant of this trope involves a dog that's an alien, however, it can also apply to other types of animals, and "alien" can be substituted for virtually any sentient fictional species.

Examples of The Dog Is an Alien include:

Advertising

A Budweiser commercial opens with a dog coming out of a house. It runs to the middle of nowhere and gets taken on board an alien ship. The ship takes the dog to the alien leader's quarters on another planet, where the dog presses a button on its collar and reveals that it is actually an alien in disguise.

Comics

The comic book story "Rover's a Good Dog!" from Forbidden Worlds #106, which is about a race of evil alien dogs sending an agent out in the guise of a domesticated Earth dog to photograph the plans of a top-secret American weapon. However, the agent becomes compassionate to the inventor and his family, and ultimately doesn't have the heart to go through his mission, instead sacrificing himself to save the family.
In The Incredible Hercules, we find out that Kirby, the coyote pup that Amadeus Cho had adopted, had been long-replaced by a Skrull imposter. While the real coyote was safe and unharmed, the Skrull!coyote had accompanied Cho for the better part of a year before The Reveal.
Krypto the Superdog
"My dog's a [mystically cloaked] genetically engineered psychic dinosaur from the 87th century."

Film

Stitch from Lilo and Stitch pretends to be a dog despite looking more like a blue koala.
Frank the Pug from Men in Black. The Animated Series revealed that under his dog suit he looks like a green dog. Also he is apparently prone to dog like behavior and it's not part of the disguise.
In I Am Number Four, John/Number Four's dog Bernie Kosar shapeshifts into a more monstrous, distinctly more extraterrestrial creature (that still resembles a dog) known as a Chimera to pull a Big Damn Heroes, engaging another alien monster in combat and eventually killing it.
Subverted in The Cat from Outer Space, in which the alien looks exactly like a cat in his natural state and doesn't do much to pretend to be one except refrain from speaking. If the humans assume he's a cat, it's not his fault.

Literature

In the short story, "Puppet Show", by Fredric Brown, an old prospector brings a very ugly Rubber Forehead Alien out of the wilderness on muleback, and the captive is questioned by the military. After a bit of subterfuge, it turns out that the captive is a robot, and the prospector declares himself to be the real alien. The interrogator expresses relief that the master race of the galaxy looks human after all... at which point, the prospector reveals itself to be a robot as well, and the mule asks what a "master race" is and why its appearance should matter.
Trillian's mice from The Hitchhiker's Guide to the Galaxy turn out to be aliens in disguise. So are all other mice, wild ones included, but Trillian's are specifically implied to be albino laboratory rodents, hence domesticated.
The alien in The Thing masquerades as a dog for a while.
In John Scalzi's Agent to the Stars, the gelatinous Blob-like alien the protagonist meets eventually takes on the form of a dog in order to come off as more appealing to humans.
Literal in Animorphs, where the Chee bonded the essence of their Pemalite masters to wolves to create dogs.

Live Action TV

ALF did this from time to time, with varying degrees of success. For instance, on one occaision, he was seen by a hobo who thought he was a kangaroo... and promptly leapt off the train they were riding.
In Supernatural there are Skinwalkers who can take the form of a dog. One of them becomes attached to the family he lives with.

Music

In his song "Midnight Star", one of the articles that "Weird Al" Yankovic sings of seeing in the titular supermarket tabloid is "Your pet may be an extraterrestrial!" (Amusingly, this was inspired by an actual article printed in the National Enquirer a few years earlier.)

Video Games

In Legacy of the Wizard, Pochi looks like a dog when hanging around the family home, but when selected as a playable character he turns into something that is definitely not a dog.

Western Animation

Conan the Adventurer: While not an alien, Needle, a baby phoenix, would occasionally pretend to be a parrot to avoid drawing attention.
The cat in Kid vs. Kat is an alien that looks like one of those hairless cats.
Princess Celestia's pet phoenix in My Little Pony Friendship Is Magic is a prankster and pretends to be a rather sickly parrot, much to Fluttershy's consternation.
Invader Zim: GIR disguises himself as Zim's pet dog. ... his disguise being a lame costume with a zipper and a tongue sticking out.