Usagi Tsukino from Sailor Moon. Even her name means "rabbit", and her hair is meant to mirror the ears of one. This relates back to the astrological motif as well, from the Japanese myth of the rabbit on the moon. Chibi-Usa is designed to look even more like a rabbit, with her pinkish eyes and bunny ear-shaped Odango.
From XxxHolic, we have Yuuko who is often represented by a butterfly, which symbolizes change and how she changes her customers, including the main characters.
Also life and death, to reflect her undead nature.
And fate, of course.
And Watanuki is often represented by Foxes and/or birds.
Being an anime about ballet and fairy tales that was heavily influenced by Swan Lake, Princess Tutu has several of these, along with references to Animal Stereotypes. In particular, Princess Tutu is heavily associated with swans (as is Mytho in his true, princely form), the girl that transforms into her is named Ahiru ("duck") and is really a duck disguised as a human, the villain is a Raven and thus crows are associated with evil and the bad guys, and Princess Kraehe ("crow" in German) is associated both with crows (obviously) and black swans. The opening intro goes as far as to show Ahiru in her duck form flying into the sky as she transforms into a beautiful swan—an "Ugly Duckling" reference that has not been lost on the fandom.
In One Piece, the original Seven Warlords of the Sea have an animal in their names and can often identify with the animal's characteristics:
Dracule Mihawk: the Hawk, having sharp, narrow eyes, similar to those of a hawk.
Boa Hancock: the Snake, being beautiful and vain. She also resides on an island where serpents are the pet of choice.
Bartholomew Kuma: the Bear, appearing to be frightening and extremely large.
Donquixote Doflamingo: the Flamingo, wearing a pink, flamboyant clothes and walking like a flamingo.
Gecko Moria: the Gecko, his clothing resembling a gecko.
Alternatively, the Bat, given his general shadow theme, and that his name is very close to, or at least contains, the Japanese word for bat (koumori).
Crocodile: the Crocodile, keeping monstrous crocodiles as pets and having a scar that resembles a crocodile's smile
Luffy is a monkey, happy-go-lucky and hyperactive.
Zoro is a shark, terrifying and hard to approach.
Nami is a cat, sly and sneaky.
Sanji is a duck, loud and loving.
Usopp is a armadillo, frightened easily and defensive.
Robin is a crane, tall and graceful.
Franky is a bull, boisterous and short-tempered.
Brook is a horse, affectionate and friendly.
Additionally, in One Piece: Unlimited Cruise, each of the Straw Hats had their own animal-themed costume:
Luffy: Lion
Zoro: Dragon
Nami: Tropical Fish
Usopp: Owl
Sanji: Goat
Chopper: Dinosaur
Robin: Butterfly
Franky: Rhinocerous
Brook: Swallow
The same goes forthe members of the CP9:
Spandam is a Panda.
Rob Lucci is a leopard.
Kaku is a giraffe.
Jabra is a wolf.
Blueno is a bull.
Kumadori is a lion.
Fukuro is an owl.
Kalifa is a sheep.
Nero is a weasel.
And a few other characters, like Mr. 2 (a swan), the marine captain Nezumi (a rat) and of course, every Zoan user (their respective animal).
Katekyo Hitman Reborn takes this concept to the logical conclusion. It is easier to list the amount of characters who don't have an animal associated with them. That number is 0.
In Chrono Crusade, Aion is often associated with birds, particularly an eagle that is his familiar. He often sends his eagle ahead of him to communicate with others or make his presence known. He also refers to Chrono as "my bird who can't fly", and even goes as far as to describe a character falling into his trap as a "turkey flying into the oven basted and ready to cook."
Black and White from Tekkon Kinkreet are collectively referred to as 'the cats,' and White is often seen wearing hats or hoods that mimic animal looks.
The animals in Pet Shop of Horrors are usually connected to both their owner's "fatal flaw" and a possible means of redemption. The man who deceived his new bride gets a highly possessive (and hungry) mermaid; the selfish drifter gets a sweet little kitten to soften his nature.
In Lucky Star, the characters themselves start wondering about which animal motif suits them best. Joking unflappable otaku Konata gets a fox, cute and innocent Tsukasa a puppy, soft-mannered and peaceful Miyuki a sheep (although Konata would quip that she's more suited to a cow due to her...ahem... bust size)... and resident Tsundere and Straight Man Kagami is to her endless shame given a bunny (due to her underlying emotionality and her tendency to hide it from the world, and, apparently, because her ponytails look like rabbit ears according to Konata).
Rurouni Kenshin is full of animal motifs: Kenshin is the Dragon, Sano the Rooster, Saitou the Wolf, and Enishi the Tiger. It also makes an extended joke concerning women's face shapes: in Japan, women are considered to be Tanuki ("raccoon-dog", round and open features, implying naivete) or Kitsune ("fox", long and narrow, implying mischief). When Saitou meets Misao for the first time, he has an Imagine Spot: If Kaoru = Tanuki and Megumi = Kitsune, then Misao = Itachi (weasel). Misao was not pleased.
Ikki from Air Gear is often compared to a crow, both by other characters and through imagery.
The witches from Soul Eater: not only do their motifs tie in with their outer appearances and powers, but a good deal of them have tie-in names as well:
While Free is male and not necessarily a witch, he does have a multitude of magical powers and has a wolf motif.
Another male non-witch character, Eibon/Noah, can be presumed to have a worm motif, since "worm" is in his chanting and since he used one to bite an enemy to pieces. The fact that he wields a book, specifies it as a (badass?) "bookworm".
In Berserk, Griffith is closely associated with the hawk; besides the name of the group of his followers, The Band Of The Hawks, his helmet is vaguely similar to that of a bird of prey, he often wears a cape (symbolising the wings), and is even called "The Hawk of Light". Eventually, once he becomes a member of the Gondhand, his demonic form Femto resembles a red hawk with bat like traits. His counter part, Guts, however, is more closely associated with wolves, most notably by his "inner beast" Guts is also known as "The Dark Hawk", to counter Griffith.
Naruto Uzumaki and Sasuke Uchiha are odd cases of having two Animal Motifs each. First are ones which they "inherited" from their teachers (which are really too blatant in their cases to even count as motifs) and the second are ones unique to them. Naruto has toads and foxes (resemblance to a fox, a prankster but always keeps his promises), while Sasuke has snakes and hawks (what he names his team, an illusion he uses is represented with feathers pierces the person, he learned to summon a hawk, his hair).
Also, Itachi has a raven motif-thing going on, which is interesting if you consider that Sasuke's motif is the hawk...
The rest of the Konoha clans save for the Senju have their own, too: Hyuuga- birds, Inuzuka- dogs, Yamanaka- boars, Nara- deer, Akamichi- butterflies, Sarutobi- monkeys, Uzumaki- foxes.
Soifon's theme is the Asian Giant Hornet. She has the aggression to match, too.
Gin's theme is predominantly the snake. However, some characters also compare him to a fox because of his tendency to play pranks on people. In the end, the manga does take the snake-plus-fox theme to its logical conclusion in chapter 414 where a colour picture of Gin depicts him as Inari (more famous for being fox themed, Inari has even older, but less well-known, snake associations).
Unohana is ray-themed. Her shikai form even takes the form of a giant ray of indeterminate species. Akin to the mixed mythology of the ray as both aggressive, dangerous poisoner and killer, and a more benign healer and antidote, Unohana has been portrayed as a benign healer but hints occur occasionally that there's a much more dangerous side to her.
Komamura is wolf-themed to such an extent that he's a humanoid wolf and has the stereotypical Undying Loyalty (to Yamamoto) as well. It's a Running Gagin-universe that characters mistake him for a dog instead of a wolf which works well as the fandom often mistakes him for a dog as well. He's also got the ability to communicate with dogs, owns a dog, and has a secret weakness for human shows about puppies.
Tousen is themed on the bell cricket to such an extent that when he finally gains resurreccion it takes an insect form reminiscent of the The Fly.
Mayuri has, amongst a few other themes, a strong peacock theme from his name, to his colourful attire, to his aptitude for poisons and antidotes.
Ukitake is carp-themed. This includes the concept of the carp representing boys who can overcome adversity to become stronger. He gained an incurable lung disease as a child. Despite that, he's still managed to not just reach the captain rank but is one of the longest-serving captains of all.
Rangiku is cat themed. She takes the seductress route with her cat themes being officially the sexiest woman in the entire Gotei 13 and is also an example of The Tease. Her zanpakutou behaves like volcanic ash, conviently tying in to the concept of a slashing cat.
Yumichika is peacock-themed to such an extent that, as well as having the vanity and obsession with beauty, he's also got the less well-known folklore traits of being extremely watchful (he tends to sense reiatsu when others don't or even as fast as captains), but he also has the ability to "bind" evil, as well as having rejuvenation abilities - powers also associated with the peacock which is why the peacock overlaps the phoenix in mythology.
Yoruichi can turn into a black cat.
Coyote Starrk is wolf-themed, specifically, lone-wolf themed. Appropriately, he has the unique power of being able to split his soul into companion beings, including a large pack of very dangerous wolves.
Harribel is shark-themed. Dignified and terrifying, she comes with obligatory water powers.
Ulquiorra is bat-themed to go with his darkness, void and despair themes. His resurreccion has led to fandom-wide Batman jokes.
Nnoitra Jiruga is Praying Mantis themed. Predatory, capable of being stealthy and underhanded or a whirlwind of brute force. Also, a lot of emphasis is made on the fact that he's not as strong as a certain female teammate and one of his resurreccion tricks is to produce multiple arms (four initially, with two extra hidden for ambush purposes to bring his total to a very six).
Grimmjow Jaegerjaquez, who is jagur-themed, specifically panther (black jaguar) in keeping with the theme of him being the dark counterpart of Ichigo (who is sun and eclipse themed), who (as the jaguar symbolises in mythology) is obsessed with kingship. His sword is named Pantera and his released appearance becomes decidedly more feline. When he was a hollow, he was a cat.
Zommari takes the prize as the weirdest. He's sea urchin-themed, and his resurreccion basically turns his lower body into one full of many eyes. He shows the author did the research as the sea urchin is associated in mythology with witchcraft just as Zommari's powers are.
Szayel Aporro Grantz is a parasitic worm; strange, maybe even good-looking but incredibly vile and with a variety of powers that rely on drawing health from hurting/killing another organism. On a more fantastic level, he's also associated with the phoenix which is again appropriate for parasitic worms.
Ggio is cat-themed, specific sabre-tooth cat and tiger-themed.
Findor is crab-themed. In resurreccion his one arm even becomes a giant pincer. His powers are water-based.
Avirrama is eagle-themed, even down to having wings and feather-based attacks.
Nirgge is elephant-themed and his power lies with his physical strength.
Poww is essentially a monstrous whale that masquerades as humanoid. In resurreccion he becomes monstrously large (not that he wasn't already) and gains a throat like a baleen whale.
Harribel's three fraccions are all animal based (Mila-Rose is lion themed and has the Greek Amazon look to go with it, Sung-Sun is anaconda-themed and has snake-appropriate powers, Apacci is deer-themed. In resurreccion she is basically a deer-woman).
Tesla is warthog themed and practically turns into the warthog equivalent of a minotaur in resurreccion.
Loly is centipede-themed.
Pesche is stag beetle themed, to an extent where it's made a joke of in the manga. He's mistaken for an ant and he gets very indignant.
In GetBackers, Ban is often associated with snakes. His eyes are slitty and look a lot like a snake's, and even one of his trademark attacks is called "Snake Bite." Shido even calls him "Snake Bastard." Hey, even his proud, condescending attitude is rather reminiscent of a certain trope.
In Yu-Gi-Oh! GX, there's an animal motif on two points where Misawa and Judai clash. The artwork depicts a dragon coming from Judai, and a tiger coming from Misawa. This is a reference to tigers and dragons represented by Yin and Yang in Taoism. Dragon was Yang, and Yang went with rushing headlong into things on instinct, which is how Judai does everything. The tiger was Yin, going with thinking and planning, which Misawa does even with things like batting in baseball.
For extra giggle points, Misawa eventually falls in love with Taniya, a tiger woman, and Juudai with Yubel, who was transformed into a dragon to protect him.
Hajime no Ippo uses this trope quite a lot. Ippo is a gazelle, Sendo a tiger, Vorg a wolf, Date a lion, Woli a monkey, Kimura a dragonfish... Notably, Takamura, despite being the 2nd main character, does not have a clear motif. He could be a hawk (his name reflects it and he wears a hawk costume for world title fights), a bear (won against one and has worn his fur) or a rhinoceros beetle (wore such a costume and his K-On! manga appears to have a thing for turtles and tortoises. For one, there are the statues on the school staircases, based on the fable of the tortoise and the hare. In the opening of the first season, the girls are seen hopping over stones in a river, some of which are turtle-shaped (both are from real locations, by the way). Ui owns a large turtle plushie. And then there's Ton-chan, a turtle living in an aquarium in the club room.
The creator of Descendants of Darkness has often drawn the two main characters with animal traits, both in the manga and in extra art. For Happy-go-lucky, often childish, always energetic and loyal Tsuzuki, it's a puppy. This visual is used enough in the manga and anime that fans often reference Tsuzuki as going into "Puppy-mode". For the quiet, loner, bookish, easily angered, defensive and Tsundere Hisoka, it's a cat. While this isn't used nearly as much as the Puppy-Tsuzuki visual, it's no less apt.
Satsuki Yotsuba is commonly drawn with a Koala behind her and is the only one drawn quite different clearly inspired by a Koala.
In Full Metal Panic, during comedic moments, Sousuke's animal motif is a cute (albeit irritable looking) little dog. A more plot significant one for him, though, is a tiger (referring to the fact that he's the "son of Bdakshon's Tiger," being called "Tiger" by Gauron in the English dub, as well as his adopting a pet tiger that he loves). On the other hand, Gauron's animal motif can be seen as a dragon, derived from his name "Gauron" (meaning "nine dragons" in Chinese). Symbolism is rampant when one considers the antagonizing, spark-filled relationship between the tiger and dragon in Asian culture. In fact, the Tiger Versus Dragon trope page describes their relationship perfectly.
The various martial arts of the Nanto Seiken school in Fist of the North Star are named after birds.
Shin's Nanto Koshuken style is the "Long Eagle Fist"
Rei's Nanto Suichoken style is the "Waterfowl Fist"
Juda's Nanto Kokakuken style is the "Crimson Crane Fist"
Shew's Nanto Hakuroken style is the "White Heron Fist"
Thouzer's Nanto Ho-oken style is the "Phoenix Fist"
Haz and Gil's Nanto Soyoken style is the "Twin Hawk Fist"
The only exceptions to this theme are the Golan Colonel's Nanto Muonken style ("Silent Fist") and the knife jugglers Beji and Giji's Nanto Sozanken style ("Twin Kill Fist"), as well as most of the anime-only styles from filler episodes. However, most of the styles from the Gaiden spin-offs follow the avian theme.
In Future GPX Cyber Formula, some of racing team's logos have these. For example, Team Sugo has Pegasus as their logo, Aoi has the Griffin as their logo and as for the team Albatross DDT... well, you can probably guess what they have as their logo.
When Shinjyo uses his Peacock/Phoenix Wing boost, the fire in a shape of the fiery bird comes out of the booster's nozzles.
In the first anime of Fullmetal Alchemist after joining the military, he is constantly taunted and mentioned as being its "dog". After defecting when his brother becomes the philosopher's stone, he voices to his commander, Mustang, that he is now a stray.
The manga and second anime use the "dog of the military" motif as well, mostly as a derogatory nickname given to state alchemists by people who believe alchemists should not be involved in state affairs.
In Spirited Away, all the characters from the spirit world are actually animal spirits, according to the Word of God. Lin is a weasel. Kamaji is a spider. Several workers in the bath are frogs and slugs. Yubaba takes the form of a dark bird, perhaps a crow. *Haku is a dragon.
In Axis Powers Hetalia, there's Greece with his many cats. He himself wishes to be a cat, and even has a cat army. Not to mention wearing cat ears in one episode (Japan put them on him), after wishing he were one of his feline companions.
As an added note, there's Usarisu. After a drawing on the author's blog of Chibirisu (the little kid version of England) with bunny ears, the trend spread of drawing little England with the ears became quite popular among fans.
In Shigurui Kogan Iwamoto and after him Gennosuke Fujiki symbolise the Tiger while Seigen Irako symbolises the Dragon.
Most of the superheros in Tiger and Bunny have an animal motif. Kotetsu is a tiger, Antonio an ox, Nathan a phoenix, Pao-Lin a dragon, and Barnaby has the honor of being frequently alluded to a rabbit. He is not amused by this.
In Ao No Exorcist, Konekomaru is one of the main characters to be this. Part of his name, Neko, means cat. He loves hot milk, he hates being cold, and he is one of the smallest and cutest characters in the series.
On the other side of the spectrum, Mamushi Hojo is incredibly snake-like. She is very sharp tongued, condescending, and slippery like one; her name means pit viper; she even has the slitted snake-pupils for God's sake!
Slam Dunk uses this trope pretty frequently in combination with chibi. Centers that are big and ugly are nicknamed some variation of "gorilla" (Gori, Bald Gori, Ape King), while someone whose annoyingly energetic is called a monkey (Redheaded Monkey, Wild Monkey). Similarly, Shohoku is often portrayed as a team full of monkeys who follow a Gorilla, with the exception of Rukawa whose called a fox.
Eyeshield 21 has Monta with an uncanny appearance to a monkey. Patrick "Panther" Spencer is known to be one of the fastest people in the world. Blood Knightberserker Gaou is comparable to a Tyrannosaurus with the way he "devours" anyone who stands in his way. Rui has the appearance of a chamelion.
In Kodomo No Jikan (manga only) Kuro is occasionally drawn as a black cat (and in both anime and manga she often sports/sprouts cat ears) and Mimi is drawn as a white rabbit. Also, Aoki compares the cat he had been feeding to Rin. When it scratched him, she justified it by saying that it might have been abused.
The Cocoon manga has lots of imaginery related to silk worms and silk moths.