Shoulder-Sized Dragon

"Who's the cutest little Smaug? You are! Yes you are!"

In folklore, both Eastern and Western dragons are invariably gigantic. In modern fantasy, however, it's common to see miniature draconic creatures as well. These are usually around the size of crows or hawks, but otherwise resemble standard Western dragons. They can almost always fly, but they may or may not be able to breathe fire and/or use other magical abilities, and like their larger cousins, they may or may not be sentient and able to speak. They're mostly harmless and usually rather cute -- Reptiles Are Abhorrent almost never applies. Settings that have these critters usually have full-sized dragons as well; occasionally, a Shoulder-Sized Dragon may even just be an ordinary dragon hatchling that has not yet attained its full size. More commonly, though, they're a separate but presumably related species.

Why? Well, when it comes to Badass Adorable Non-Human Sidekicks, it doesn't get much better than a pint-sized version of Smaug. In any work where these creatures exist, one of them will be kept by a major character as a pet, Familiar or Bond Creature. The trope name comes from the fact that they are almost invariably found perching on their human companion's shoulder in the Parrot Pet Position.

As far as we can tell, the Ur Example of this trope is found in Ursula K. Le Guin's 1968 novel A Wizard of Earthsea, in which tiny "dragon-lizards" that can be tamed as pets appear briefly. The Trope Maker, though, is probably Dragonquest by Anne McCaffrey, published three years later, in which the 'Shoulder-Sized Dragons play a much bigger role.

Subtrope of Our Dragons Are Different, Instant Awesome, Just Add Dragons, and Cool Pet. See also A Boy and His X and Loyal Animal Companion, as well as Fun Size.

Examples of Shoulder-Sized Dragon include:

Anime and Manga

Axew, a small Dragon-type Pokémon, serves as Iris' primary Mon in the Best Wishes anime, and can often be seen in her hair or hanging from her shoulder.
Magical Girl Lyrical Nanoha Striker S introduces to the franchise Friedrich, a baby silver dragon under the care of Caro. While he's in this form most of the time, he could also be unsealed to become a more adult dragon for combat and transport purposes.
Saiyuki: in dragon form, Jeep is this size.
The manga Dragon Drive has the main character partnered with a pint-sized dragon that looks to be a loser at first, but is revealed to be more useful than he seems.

Comic Books

Kitty Pryde of the X-Men has a roughly cat-sized pet dragon (actually, a dragon-shaped extraterrestrial) named Lockheed.
In The Skull of Agarash, a graphic novel set in the Lone Wolf world, Captain Khadro, pirate ruler of the Lakuri Isles, has a small winged reptile looking like a tiny dragon as Pirate Parrot. It is in fact a Liganim, the shapeshifting Familiar of a Nadziran, the Black Wizard currently possessing Khadro.
In Kurt Busiek's Arrowsmith (World War I in a world governed by magic) soldiers bond with small "dragonets" by means of a rare mystical metal. This bond allows the soldiers to fly with their dragonets perched on their arms like hunting falcons.

Fan Works

In the Worm/Luna Varga crossover Taylor Varga, when Taylor and the Varga make a breakthrough that allows them to manifest multiple bodies, one of Taylor's favorite variants is a foot-and-a-half-long version of Toothless from How to Train Your Dragon -- in which she naturally perches on shoulders and heads.

Film

Mushu in Mulan is a rare example of a shoulder-sized Eastern dragon. Justified in that Chinese dragons are said to be able to change size at will. Disney had originally intended for Mushu to be gigantic, but felt he would be terrifying to children, so they scaled him down to make him look friendlier and not as scary.
The Terrible Terror dragons from How to Train Your Dragon.
The short film Sintel features the main character's pet dragon, Scales.
In the Brave Story movie, the baby dragon is a small, fluffy creature that's perfectly Head Pet-sized. He fits the "immature version of larger species" subtrope. However, in the book, instead of being the Team Pet, he's a much larger one-off creature who serves an Androcles' Lion purpose.

Literature

The Dragonriders of Pern novels by Anne McCaffrey have fire-lizards, which are native to the planet Pern and evolved the ability to exhale pyrophoric gas as a natural defense. While they have normal animal-level intelligence, they're weakly telepathic, and their instinct to imprint on whoever feeds them upon hatching makes them natural Bond Creatures. Human colonists genetically engineered fire-lizards for greater size, intellect, and psychic ability, producing full-sized dragons.
In Ursula K. Le Guin's Earthsea series, they're called harekki, and Yarrow keeps one as a pet. (In this case, they're smaller than usual, growing no bigger than a human hand; Yarrow's usually coils itself around her wrist.)
The Dragaera books have small venomous flying scavengers called jhereg. They're cold-blooded, don't breathe fire, and resemble miniature wyverns rather than standard dragons. While they cannot speak, they are fully sentient, due to genetic tampering in the distant past. The main character in the books keeps a jhereg as a Familiar.
The swamp dragons of the Discworld grow to about two feet in length, are commonly bred by the wealthy as pets, and can be trained to perch on shoulders—Lady Sybil Ramkin breeds shoulder-sitters as a popular fashion accessory. Since swamp dragons tend to react to stress or severe indigestion by spontaneously exploding, however, it's not really a good idea.
In A Song of Ice and Fire, Dany has three, of the hatchling variety. They grow out of Shoulder Dragon size range pretty quickly.
In Tamora Pierce's The Circle Opens quartet, an untrained lightning mage who works as a glassblower accidentally creates a living glass dragon, about an arm's length in size. Tris, one of the main characters, decides to keep it as a pet and names it Chime.
Kale's minor dragons from the Dragon Keeper Chronicles.
The Cardinals Blades by Pierre Pevel features dragonnets, which are exotic pets favoured by the rich and powerful.
There's a Shoulder-Sized Dragon named Mulberry in the novel Red Wizard by Nancy Springer. In this case, they don't seem to be a naturally occurring species; Mulberry was accidentally called into existence by an inexperienced wizard.
In the Flinx and Pip novels set in Alan Dean Foster's Humanx Commonwealth setting, the main character has one of these. It's a sci-fi setting so Pip is an alien and can't breath fire, but she fulfills all other features, being essentially a spitting cobra with hummingbird wings and a psychic link to her master.
The Year of Rogue Dragons has Jivex, the fairy dragon. Unlike most examples of this trope, in his own way Jivex is actually pretty badass.

Live-Action TV

In Primeval, Abby's pet Coelurosauravus, Rex, is basically the dinosaur version of a shoulder dragon.

Newspaper Comics

Growf in What's New with Phil and Dixie.

Tabletop Games

Dungeons & Dragons
- Pseudodragons, which are tiny dragons that can sometimes be used as pets or familiars.
- Fairy dragons, tiny dragons with fey blood, butterfly wings, and cheerful smiles, who love playing jokes on humans.
- Several chromatic and metallic dragon start life in the "tiny" or "small" categories.
In Blue Rose, there's a species of small dragons called "drakes," usually around twelve inches long and sometimes colloquially described as "pocket dragons". They're one of several intelligent, telepathic species of Bond Creatures. (Interestingly, if full-sized dragons exist in the setting, they're never mentioned.)
Munchkin has a Cute Shoulder Dragon that gives a +2 bonus to male players and +4 to female players.

Toys

Folkmanis, a puppet-making company, has two dragon puppets that perch on your shoulders. One is red and the other purple.
Similar dragon puppets or plush toys designed to sit on a person's shoulder are often sold as an accessory at Renaissance festivals.

Video Games

Dragoons in Final Fantasy XI get to summon pet wyverns, which are roughly the size of eagles.
Most unevolved Dragon Pokémon are this.
Players in World of Warcraft can acquire dragon whelps (that is, hatchlings) as non-combat pets. In addition, NPC dragons in the game come in almost a dozen different shapes and sizes, including whelps almost identical to the pets.
Finn's dragon Steiner from Beyond the Beyond, at first.
In the My-HiME fan game Mai-HiME: Fuuka Taisen, Kagutsuchi fights side-by-side with Mai as a tiny dragon, only growing to its normal (gigantic) size when she uses certain special attacks.
Baby dragons in Lunar are the size of housecats. They also look like cats, but with wings.
Warlocks in Might and Magic have familiars. Rarely, this familiar is a dragon, not hatched until the attuning, which is the case for your Druid characters in VII.

Web Comics

In Drowtales, Ashu'athama, the Sharen headmaster at Orthorbbae, is shown with one.
In Wayrift, Zemi is a perfect example of this.

Web Original

Dragon Cave has a few among its plethora of reptilian wild-life. There are the Night and Day Glories, which are only the size of kittens when full-grown, the Sweetlings, which can ride on a human's shoulders, and several breeds of Pygmy dragons, which are housecat-sized.

Western Animation

In My Little Pony: Friendship Is Magic, a baby dragon named Spike serves as Twilight's ward and assistant. (This is a rare case where the Shoulder-Sized Dragon's companion isn't a human—but humans don't seem to exist in this world, and the ponies are basically just horse-shaped people for all intents and purposes.)
Dojo Kanojo Cho from Xiaolin Showdown, who can transform from a tiny dragon to a giant one.
Pocket Dragons Adventures. Essentially, the adventures of several, sentient palm-sized little lizards. They aren't quite shoulder-sized, but they do literally fit into your pocket!
In The Owl House, Stringbeans, Luz's palisman, is a teeny-tiny dragon.