In the Slayers universe, the "demon race" and the "godly race" are vying for control of the world. The godly race usually take on the form of Western-style dragons, but can assume human form if they so wish. Filia, a character from the third season, is a Golden Dragon that apparently isn't much used to her form as a blonde human female — her pointed tail frequently pops out from under her dress whenever she's emotionally excited (which usually tends to happen when she's in the presence of the Trickster demon, Xellos).
Though technically, Filia isn't a god herself. The Shinzoku do often resemble dragons, but actual flesh-and-blood dragons like Filia are just a mortal race that serves them. Which explains why they're so much weaker than their supposed opposite numbers, the Mazoku. The novels themselves state that dragons are far, far outclassed by Mazoku. It's actually a minor plot point in the seventh novel.
The Golden Dragons are special. Lina mentions in NEXT that Golden Dragons are some of the smallest dragons, but also one of the most magical and most intelligent. Dragons of other species they come across in the series seem to be little more than big lizards with wings and (usually) some sort of Breath Weapon, while even Lina would hesitate to go up against a Golden Dragon.
That said, even regular dragons are intelligent enough to communicate with one another. After Lina is referred to as the "Dragon Spooker" a couple of times and browbeats an explanation out of someone (viz. her reputation is such that even dragons will step aside when she passes) we're treated to a scene where a dragon comes along and starts wreaking havoc in the village...until it spots Lina and starts trying to leave as casually as possible.
Most of Yu-Gi-Oh!'s most powerful cards are in fact dragons (if not, they most likely have "Dragon" in their name somewhere). To wit: Stardust Dragon, Dark Armed Dragon, Judgment Dragon, etc. etc...
Two of the three Egyptian Gods are dragons (Slifer the Sky Dragon, The Winged Dragon of Ra, both of them are actually "Divine Beast"-monsters) and the three of the most five powerful monsters are dragons (Dragon Master Knight, Five-Headed Dragon and Malefic Truth Dragon).
In Yu-Gi-Oh!: Capsule Monsters, the fifth Trial is about slaying the five evil dragons Tyrant Dragon, Luster Dragon #2, Serpent Night Dragon, Aqua Dragon and Meteor Dragon, who later fuse to become Five-Headed Dragon (despite that Aqua Dragon is technically a Sea Serpent-type monster, so the fusion is technically illegal). Yugi and his friends get also dragons: Yugi has temporarily the Blue-Eyes White Dragon, Jonouchi has Red-Eyes Black Dragon, Anzu has Seiyaryu, Honda has Thunder Dragon (which is technically a Thunder-type monster) and Sugoroku has Curse of the Dragon.
Many trump cards of the Yu-Gi-Oh! GX characters are either dragons or have "dragon/dragoon" in their name or actually resemble dragons.
Yu-Gi-Oh! 5D's has the Signer Dragons, the main and signature cards of the heroes. They are Stardust Dragon, Red Dragon Archfield, Black Rose Dragon, Ancient Fairy Dragon, Black Feathered Dragon and Life Stream Dragon.
Yuma from Yu Gi Oh Zexal has Number 17: Leviathan Dragon, a monster that can power itself up twice, and ZW Tornado Bringer. Kite has Galaxy-Eyes Photon Dragon and his upgrade Neo Galaxy-Eyes. While not technically a dragon, Shark's Shark Drake is very draconian. Kaito's Robot Buddy Orbital 7 uses a deck with an XYZ called Googly-Eyes Drum Dragon, which is also incredibly powerful, but technically a Machine.
And then there's Yu-Gi-Oh! ARC-V, which largely focuses on dragons as well. We have Yuya's Odd-Eyes Pendulum Dragon, Beast-Eyes Pendulum Dragon, Rune-Eyes Pendulum Dragon and Odd-Eyes Rebellion Dragon, Yuto's Dark Rebellion Xyz Dragon, Yugo's Clear Wing Synchro Dragon, Yuri's Starve Venom Fusion Dragon, and Jack's Red Wyvern and Scarlight Red Dragon Archfiend. You can also count Constellar Ptolemy M7, who is very dragon-like despite being a Machine.
As do Duel Masters and its CCG. Shobu's signature card is Bolshack Dragon. Worth noting is that there are four types of dragons, including zombie dragons, not to mention "wyverns" that look like dragons but don't count as them (uh...), "Dragonoid" lizardmen, and giant reptiles called Dune Geckos. This was a CCG that was fond of horrible, destructive, scaly things.
Record of Lodoss War has at least three distinct "flavors" of dragons. Wyverns are small (read: elephant-sized), unintelligent, non-fiery, two-legged dragons that are domesticated and flown by knights. "Common" dragons are bestial, apparently wingless (there's only one shown so it's hard to judge all of them), huge fire-breathers. The Great Dragons, of which only five exist, are monsters the size of mountains with incredibly vast powers of intelligence and magical skill and close ties to the gods, who guard legendary treasures. The intro has a point that scales Humans to Wyverns then to a Great Dragonnote it starts at about 43 seconds in.
Dragon Half features Mink, a half-dragon girl with horns, tiny bat wings on her back (which somehow let her fly) and the ability to breathe fire. Her mother is portrayed as a shapeshifting red Western dragon.
Dragons in Naru Taru are about as different as they can get: baby planets shapeshifted into vaguely starfish-like flying immortal monsters with the power to duplicate any object they come in contact with who need to fuse with a human (or other intelligent lifeform) host then join with another dragon/human pairing to grow into an actual planet. And the series is still chock-full of traditional dragon lore symbolism.
In The Five Star Stories the word dragon is best read as "mysterious alien god". Despite looking more or less like typical European dragons with a few more Eastern influences & some vaguely insectoid characteristics & pretty much living like animals most of the time, they are superintelligent & telepathic (even being able to hack computers with their minds) & breathe quasars instead of fire. It is said they are actually a form of Organic Technology Superweapon created by a lost civilization. Luckily for the humans, it seems they just want to be left alone.
Magical Girl Lyrical Nanoha has Friedrich; a cat-sized silver dragon whelp (Wyvern-type body) that can grow to adult size when Caro unseals him, and Voltaire; a Kaiju-sized, humanoid, ancient black guardian dragon that can launch searing torrents of flame from its mouth and wing tips.
In Fairy Tail, its Dragons are a mix of both Western and Eastern versions, whereby their physical form resembles the Western versions but like the Eastern dragons are highly intelligent and possesses insane amount of magic that overpowers almost all humans.
Dragons were once the dominant species of Earthland who mostly regarded humans as a food source but were exterminated to the brink of extinction by a special breed of humans, dubbed Dragon Slayers, who were taught Dragon Slaying magic by Dragons who believed humans and dragons can co-exist harmoniously. There was a war, set 400 years before the manga, that pitted the dragons who subjugated humans against those who were Pro-humans and their Dragons Slayers. Except for Acnologia, those few dragons who survived lead reclusive lives away from and not meddling in the lives of humans. Only recently has the other surviving dragons become more active, by fostering and training orphans to be a new generation of Dragon Slayers in anticipation of a future war with Acnologia.
All the Dragons tend to vary in personality from what is shown in or described. Grandine was very kind and gentle. Igneel was a strict and harsh but loving parent. Metallicana was a cruel jerk than none the less still took Gajeel and raised him. Zirconis despises humans, eats them, and thinks teaching humans dragon magic should have been forbidden, but is at least willing to converse civilly with humans and will give valuable info. Acnologia attacks all humans brutally on sight and comes off as a beast despite his intelligence because he believes humans are such vermin they aren't worth the effort of speaking to despite the fact he still is human, or at least can return to his human form when he wants.
It's also possible for Dragons to be created artificially. When Dragon Slayers begin to mature and further their Magic, they eventually unlock Dragon Force, which begins to change their body's physiology more and more to that of an actual dragon, including scales and, in some cases, wing-like growths. As they mature more and more, a Dragon Slayer's body eventually starts to become more and more permanently like that of a dragon, usually accelerated by the process of killing other Dragons and bathing in their blood, until they finally become actual Dragons in form with the ability to change back and forth unless they have certain antibodies to prevent it. This was how Acnologia became what he is today, and was why Igneel, Metallicana, Grandine, Weisslogia and Skiadrum sealed themselves inside their children to prevent them from ending up like him by developing those antibodies inside their bodies.
YuYu Hakusho has Hiei and his Black Dragon spirit. It's called the Dragon of the Darkness Flame (in the English dub, at least) and is made of black fire. He usually keeps it sealed in his right arm.
Dragons are apparently little more than very very dangerous beasts in Mahou Sensei Negima!. So far, three? have appeared. One was inside the library for some reason, guarding something. Another got its face stomped on by Kaede for a bounty, and Yue took down a Griffon Dragon with barely any supplies except her magical artifact once she bothered to actually study magic. Sooo... the whole 'danger' factor is highly reduced by the fact that they're not really characters.
Then one showed up, an ancient Guardian Dragon who can match Jack Rakan in combat. Scary.
One could argue said dragon wasn't so great after all, when it was one-hit-ko'd by one of the villain's summons, at least until you consider that said summon was using literal hax to write it out of existence. Negima seems to use dragons as a way of showcasing how the characters have grown or how strong they are, as it seems that anyone that isn't at least a fairly important or relevant character very much hesitates to face off against one (Eva actually gets really angry at Negi when he asks early on how much training he'd need to fight one).
Dragon Ball has Shenlong, the Earth's dragon and a definite Eastern dragon, with a long, slender body, tiny arms and legs, brown horns, and a green mane. He doesn't seem that great of a fighter, although he has the power to grant wishes if someone assembles the show's titular MacGuffins. He also speaks in an older dialect, which implies intelligence. A dragon named Polunga is seen on another planet who is more humanoid and is more powerful than Shenlong.
In Dragon Ball GT Shenlong is corrupted and each dragon ball turns into a Wicked Dragon, most of which were vaguely reptilian humanoids that could cause planets to self-destruct just by existing.
Spirited Away: Haku AKA the spirit of the Kohaku River is an Eastern Dragon that's able to take on a humanoid form.
Digimon has several species who are considered dragon and are distinguishable by the suffix dramon(Though not always, most predominantly in the "Four Great Dragons" family.) in their name. Dragon-like Digimon tend to be partnered up with the main character.
Their appearance are also non-consistent with almost anything, Davis's Digimon in Digimon Adventure 02, Veemon, is a humanoid (if rather short) blue dragon-type Digimon, with two legs, two arms and a tail. Or Guilmon, partner of Takato's in Digimon Tamers, who's a red dragon-reptile-like Digimon with two arms with three claws, and two legs, also having three claws. Pretty crazy.
The "Four Great Dragons" group consists of Magnadramon◊ (who was formerly a cat at one point in its lifespan), Megidramon◊ (the evil-aligned final form of aforementioned Guilmon), Goldramon◊, and Azulongmon◊, the last of whom looks most like a traditional dragon (of the Chinese variety). As Digimon are said to be born of computer data about things from the human world, it makes sense that so many kinds of dragons would be present in the series.
Bleach has Hyorinmaru, a zanpakuto, generated from the soul of its user, and while they provide the majority of abilities for their masters, the Zanpakuto are beings unto themselves, often sharing similar personality traits as their masters, and more than a few seem to represent their respective masters' inner, repressed feelings. Here's an example; being the zanpakuto of Toshiro Hitsugaya, Hyorinmaru is an ice dragon, apparently one of calm, gruff wisdom, while Hitsugaya himself is a mature, but grumpy dude that is actually more emotional than he'd like to let on. While in his human form, Hyorinmaru is calm, quiet and obedient, whereas Hitsugaya is irritable and more prone to temperamental outbursts than his ice dragon mentor.
However, even the golem type ones are considered as powerful creatures that only strong and skilled mage/witch can summon.
In Rave Master, dragons originate from a dragon clan, which are Lizard Folk until a certain age, at which they either pass a test (and become human looking) or fail it (and turn into a feral dragon.) Appearance wise, they are western four legs two wing style.
The Vision of Escaflowne's dragons seem bizarre to modern audiences, sporting only two limbs(webbed to the bodies like a squirrel, in lieu of actual wings), blade-tipped tails, somewhat pudgy bodies and snakelike heads, but these animalistic, fire-spitting beasts are probably closer to the dragons of traditional Western folklore than just about any other anime. Also, their hearts are used to power giant robots. That part's not so traditional.
The dragons shown in the Anime are known as Chiiryu (Literally Earth Dragons), further reading has that there are three tiers of dragons, Chiiryu Suiryuu and Tenryuu, for the land, sea and sky respectively and that each one is infinitely more powerful than the last. Also while the Chiiryu borrow from western dragons the Suiryuu are more traditionally eastern type dragons (they can be seen in the architecture of Asturia).
Ryuujin the Dragon God in Yaiba is supposed to be the classical, huge eastern dragon. He actually has a human avatar as a Bad Ass samurai warrior. His true form is revealed when Yaiba uses the full power of the Orb of Ryuujin.
Several Mechanical Beasts from Mazinger Z resembled dragons, and the aspect and weapons of each one of them was different: Gelbros J3 looked like a bypedal dragon with three heads could shoot heat waves, soundwaves or acid streams: Drago Omega 1 resembled an Eastern, flying dragon shoot missiles...
Combattler V: Kiiru, the "Slave Beast" showed up in episode 9 was Garuda's dragon pet (Let me stress this: Garuda's pet was A FREAKING DRAGON). She resembled an eastern dragon, with antler horns, long whiskers, rectangular snout and a long, sinuous body. She could breath fire from her mouth, shooting beams from her eyes and regenerate herself. And it was a Mama Bear, too.
Sgt. Frog has two instances of dragons, with the main alien cast transforming into dragons with missiles, dragons with energy blasts, even a ninja dragon with a BFS.
In A Certain Magical Index, if anyone makes the mistake of trying to depower Touma Kamijou by cutting off Imagine Breaker, his Anti-Magic / Power Nullifier right hand, a massive dragon called "The Invisible Thing" will emerge from the stump. It turns out that Imagine Breaker was actually a seal that kept the dragon sealed within Touma's body. It is one of the most powerful beings in the Toaruverse.
References are also made to "St. George's Dragon" by the magic side. The being actually called DRAGON later in the story is, however, Aiwass, mentor of Aleister Crowley and the most powerful being in the series seen so far.
The first filler arc of One Piece revolves around an elderly dragon, which looks more like a gigantic bird. And that's when it's not curled up into a big ball of feathers, which is the position it spends most of the arc in.
In chapter 655 the crew has now run into a giant western style dragon which can apparently talk. Except it turns out that it wasn't the dragon talking. It was a set of human legs with no upper body or head that can talk and had been attached to the dragon..., thanks to Trafalgar Law.
Later they encounter a small talking Eastern style dragon who is actually the son of the samurai they met earlier. He ate an artificial Zoan type Devil Fruit that turned him into a dragon.
Demon King Daimao has Peterhausen, a ridiculously large western dragon that breathes drills and missiles.
Drago from Bakugan, who can actually curl up into a tiny ball when he is not fighting.
Well, let's not sugar coat it. This anime is full of this! Dharak, Rubanoid, Plitheon, Avior, Wayvern, Naga, Percival, Hydranoid, and Helios are all dragons or dragonn-like beings.
There are a lot of dragons in High School Dx D and are considered to be the most powerful race in-universe. Issei, the protagonist, is considered as one even though he's still a human-devil hybrid (he was killed at the beginning of the story thus reincarnated to a devil) because he has a dragon sealed in his left arm named Ddraig, a Welsh dragon.
Many of the more powerful cards in Cardfight!! Vanguard are dragons, and many characters have used at least one at some point. Most of the Kagero and Narukami clans are outright dragon-themed, and Tachikaze make heavy use of Dinosaurs Are Dragons.
Melan from DokiDoki! Precure is a fairy who looks like a tiny turtle lady, but can transform into a powerful Western-style dragon. She also defeats the five Pretty Cures twice to test them.
Cross Ange is all about a group of normal girls forced to fight dragons in Cool-But-Unreliable Mecha in a world that HATES them. The dragons as they seem are alien enough, using rifts to cross dimensional barriers and armed with a ranged-biological arsenal that rivals the latest in advanced technology. Then the second half of the anime comes along and it turns out that the miniature dragons are female were-dragons and are biologically compatible with the mega-giant alpha males. Their ancestors genetically augmented themselves after World War 7 and the Big Bad decided to steal their supreme leader for use as a mana reactor, AURA. The kicker is that magic in Ange's world (which hates her because they can use magic and she can't) is powered by none other than the efforts of Ange and company, as killing dragons powers the reactor.