In universe, the dragons vary from nation to nation, mainly by facial differences (length of head, horns, etc). Jake, being a mixed-race character, in dragon form shows markings of both traditional Western and Eastern dragons, whose dominance depends on the season. In season 1, he had a more Western body type (big and buff) with a longer Eastern type head; in season 2, he strangely reverted to a more long and skinny Eastern style body, with head and face now little more than his human self, just dragonized. There's also rules of magic, (silly) dragon diseases, and the rule that dragons are the protectors of the magical world.
Adding to its egregiously long list of Mix-and-Match Critters, dragons on the Asian-influenced Avatar The Last Airbender are a hybrid of Western and Eastern dragon types. They are like eastern ones except they have wings, are associated with fire and are kept by humans as a means of transportation, and appear quite intelligent. It later turns out that they are thought to be extinct, since people started hunting them to get the title "dragon", and are actually the source of firebending.
Additionally, the Sun Warriors claim that fire, particularly that which the sun is made of, is the source of life as it produces the heat necessary to live. That means, at least philosophically, that The Last Airbender's dragons breathe both fire and sheng chi.
Not to mention Wan Shi Tong, which is a strange owl-dragon hybrid.
The Legend of Korra confirms that dragons were in fact the beings that taught Wan, the first Avatar, how to firebend without the use of the Lion Turtles. Later, one appears in Season 3 which looks more Western than Eastern under the command of Zuko, implying that the species is also recovering.
There are quite a few Transformers who transform into dragons, despite real dragons generally (but not always) being nowhere to be seen. Aside from all being Western-style dragons, they're as different as the individuals that turn into them.
Of particular note is Transformers Prime, in which human myths about dragons were inspired by the remnants of a number of Predacon clones that were dispatched to Earth thousands of years ago. Prime Predacons all have draconic alt-modes.
Sonic Sat AM had a frankly bizarre interpretation of dragons. Basically, take bits of every animal that lives in Australia (including a pouch), stick them together, add giant creepy lips and a nose ring, and there's Dulcy the dragon. She's clumsy, but then again, she's young. We see her as a child briefly in "Blast to the Past Part 2", so she's in her early teens in present day at best. The older female dragon the Freedom Fighters meet and save in "Dulcy" is far more mature. Also, some - but not all - dragons can control the elements, and are called "Protectors". The only dragons shown have been female, so whether it's a Gender-Restricted Ability is unknown.
The animated feature Hellboy: Sword of Storms apparently set out to make its dragons as different as possible, stretching the definition of "dragon" a bit further than it could go in the process. Everything from human-sized, human-shaped ogres with lightning powers to unimaginably huge, squashy undersea demons are identified as dragons. This might not have been so jarring if the audience saw anything onscreen that anyone off the street would call a dragon.
Note that these creatures were all called "Dragons" as more of a title than an actual description. They were all relatives of the Ogdru Jahad, who were also known as the Seven Dragons (not that they are anything like dragons either, although they do have a few Dinosaur-like characteristics).
Hellboy has also fought regular dragons in some of the spin-offs, including The Dragon Pool, which features a Eastern-style dragon who breathed fire. As well as, in typical Hellboy fashion, his zombie offspring and the result of his long-ago breeding with humans. He also fought & defeated (sort of) the St. Leonard Wyrm, which looked more like a cross between a giant python & a saltwater croc than anything.
If Hellboy stretched the definition of "dragon", the short-lived series The Dragon Slayers broke it. It did have a few traditional dragons. It also had big giant warty hoglike things, floating blobby tentacled things, and one of the main characters was a "dragon" who was basically Ren with a couple of horns for garnish.
The comparatively better-known Dave the Barbarian similarly had a small dragon who looked like a winged pig. It also had more conventional dragons. Faffy himself was routinely referred to as a "flying potato" and noted to be pretty pathetic by dragon standards.
The main antagonist of Jackie Chan Adventures, Shendu, is a dragon, a demon one at that. He has traits from both the Western and Eastern aspects of dragons, which is probably not a surprise given that it is a Western show that has an emphasis on Eastern traditions. Even stranger is how his statue in the early episodes is a traditional Chinese design, long and swirling, but his actual form is the mixed form above. However, he is a shapeshifter. That might explain the difference between his spiritual and physical form.
My Little Pony: Spike actually learns this as an Aesop in "Spike's Search". Additionally, the dragon (though he is curiously never referred to as such) in "Through The Door" is literally just a Punch Clock Villain (they really like that trope) and is very Emo about having to be the bad guy all the time.
Spike aside, My Little Pony: Friendship Is Magic has a standard Western dragon in the episode "Dragonshy", and another one in "Owl's Well that Ends Well" who has the added features of retractable claws and tail spikes. The sea serpent in part 2 of the pilot has an overall design very similar to Eastern dragons. Both dragons hoard gemstones and riches in their caves, which actually makes sense here given that, as Spike proves, this version of dragons' preferred diet is gemivorous.
Additionally, dragons seem to age quite slowly but live a very long time. Spike's personality fits a kid of 8-10 years old, and the canon timeline supports him having lived about that long, but he's still tiny enough to ride on Twilight's back, and chubby as a toddler; the ponies all refer to him as a 'baby' dragon. Meanwhile, the dragons we meet in "Dragonshy" and "Owl's Well That Ends Well" are gigantic enough to swallow a pony in one bite (in Fluttershy's words), and apparently, sleeping for one hundred years only qualifies as a nap.
The episode "The Secret of My Excess" shows that draconic maturity is related to greed and hoarding, the more they hoard the bigger they get and giving it up makes them shrink.
The episode "Dragon Quest" features Spike going on a great dragon migration to find out about himself. The episode shows dragons of different colors and shapes and sizes, some with horns and some with spikes and more, showing there's more variety of dragons in Equestria than previously thought.
In G3 Spike mentions waking up from a 1000 year nap, but he still looks like a baby. That really makes you wonder how dragons age..
In the pilot for the G1 series, Tirek has some dragon-like animals named Stratadons which looked like no other dragons in the series.
From Xiaolin Showdown, Dojo, is a Eastern Dragon in a Western Animation. He spends most of his time in a very small form, but can shift into a wide variety of shapes, and serves as the team's transport. "Wide variety" includes "he once transformed into a working subway train".
Wakfu, who shares the universe with the MMORPG Dofus, takes a different way. The god Osamodas, creator of all living things, once had three mythical dragons, who shaped themselves into the world of Dofus. Therefore, there were other dragons, about a dozen, who were strong powerful creatures of magic and had the power to create the eponymous Dofus, magical dragon eggs. Nobody knows how many have survived to the cataclysm which leads to Wakfu, but we can see at least one in the series: Grougaloragran, dragon of fire, shapeshifted as an old man, who brings The Hero to his adoptive parent.
It gets worse: those dragons can also lay Eliatrope Dofus, a single egg which contains a baby dragon and a baby human, the latter gaining teleportation-related powers. And yes, Yugo, The Hero, hatched from one of those eggs.
As the name suggests, Dragon Hunters takes this trope and runs with it. Gwizdo and Lian-chu, the titular hunters, go after a number of different kinds of dragons over the course of the series, and no two alike. With all the variety, it seems most likely that any creature that is threatening enough to make a village hire hunters to get rid of it is labeled a "dragon" for simplicity's sake.
And then there's Dragon Tales... Flying dragons with pouches in which they store things. One two-headed dragon is a type of conjoined twin.
Bo on the Go also takes the "dragons are reptile-marsupials" approach.
Bartok the Magnificent: The villainous Ludmilla's unwitting transformation into a fat, pink, three-horned, wingless dragon during her Villain Song (see here) after drinking Bartok's potion, which turns the drinker into whatever they truly are, deep inside. Being EXTREMELY vain and caring about her own beauty and lust for power turned her into a dragon based on her personality. Somewhat related to Maleficent's transformation in Sleeping Beauty, except more comedic and less threatening (she was defeated by a freakin bat for crying out loud! At least it took a bunch of magical fairies and an enchanted sword to bring Maleficent down).
The Pirates of Dark Water featured dragons (or rather "Dagrons"), but they were apparently exceedingly rare. Dagrons were pretty much your standard green Western dragon critter. One episode featurd a magic cowl that would turn the wearer, physically and mentally, into a dagron.
In the Rupert The Bear stories Tiger Lilly keeps a small, eastern dragon as a pet.
The eponymous dragon in Potatoes and Dragons can't fly, and its body and head are just kind of a green lump with stegosaur-like spikes. It also has an irrational hatred of crowns for some bizarre reason.
DuckTales! (Whoo-hoo!) Tales of derring-do, Bad and good luck-tales!
In Son Of The White Mare, the three dragons are part of the ancient evil released out of curiosity by the brides of the progenitors' three sons. They bear resemblence to the multi headed humanoid dragons from Hungarian folklore, but strongly deviate from the traditional depictions. The three headed dragon is a massive golem of rock and lava, the seven headed is a Military Mashup Machine that looks like it several world war 2 german tanks welded togerther while the twelve headed dragon looks like a cross between a modern day metropolis and a giant computer mainframe.
One episode had the Genie build a mechanical dragon to test Aladdin's bravery. Unfortunately, Genie accidentally destroys the remote used to control the dragon, and as a result the mechanical dragon starts to malfunction and goes on a rampage.
Another episode revolved around two twins, one good and one evil, that could magically fuse together to form a Chinese dragon. Whoever initiated the fusion would gain control of the new body, and so the evil twin constantly sought the good twin to form the evil dragon body and wreak havoc. By the end of the episode, Aladdin and his friends teach the good twin to stand up for himself, causing him to overpower the evil twin and form a good dragon for the first time.
One rather odd episode of Garfield and Friends was about Garfield and his owner Jon Arbuckle ordering food at a Chinese restaurant when the waitress noticed that Garfield was actually eating too much food. She then cautions Jon by telling him an ancient Chinese folktale about an evil dragon who threatened a nearby village to completely relinquish their food otherwise he will set their village on fire. A big tiger-striped cat challenges the dragon to an eating contest in order to get the villagers' food back and wins. The dragon gets very furious and starts chasing away the cat, and while everyone's food has finally been rescued by the cat, both the dragon and the cat were never seen again. After she is finished, the waitress tells Jon that if the orange-and-black cat's descendant (in this case, Garfield himself) eats too much, then the dragon from the folktale will have his revenge. The episode ends with Garfield and Jon leaving the restaurant, while the dragon looks on while disguised as a paper dragon.
Dragons: Riders of Berk, the Sequel Series to How to Train Your Dragon, features dragons shown in the film as well as new ones. (though some of the new dragons were mentioned or shown in the book of dragons in the film) The dragons all fly and breathe fire, but there is still a huge variety. The Deadly Nadder shoots spikes out of its tail, the Monstrous Nightmare can set itself on fire, and so on.
In Blackstar, the title character's steed, Warlock, is a clear hybrid of equine (general body plan, posture, forward-bending front knees, "mane") and draconic (green skin, batlike wings, sharp teeth, fire-breathing) traits.
On Ivor The Engine, which was mostly a slice-of-life story with no obvious fantasy outside of Ivor's implied sentience, Jones the Steamer finds a strange rock by a volcano outside of Llaniog. When it's left in Ivor's firebox, it hatches into a dragon; "Not one of your lumping great fairy-tale dragons, but a small, trim, heraldic Welsh dragon." His name is Idris, and he comes out of the volcano to sing with the town choir on occasion.