Considering that Princess Tutu is influenced quite a bit by the ballet version of Swan Lake, it's probably no surprise that the anime indirectly references this legend, as well. Tutu sometimes appears as a swan to people, and was in love with the Prince from her fairytale—but she's the one who has to hide something, instead of the Prince.
Tears to Tiara uses a variation on the selkies, Llyr is a 'sea elf' who uses a seal pelt to transform into a seal. When Awarn accidentally burns it, she announces she is his wife (sea elves give their husbands their pelt, or must marry anyone who steals it).
Setsuna of Mahou Sensei Negima! is, in fact, a Half-Human Hybrid of the Tengu variety; after revealing her tengu traits she tries to skip out (per 'law of her people' and probably personal insecurities) on the crew. Negi convinces her to stick around.
Crane Wife is parodied in Hare + Guu, where Guu offers Hare shaved ice in the middle of a snowstorm, he gets pissed off. She goes into the back room, telling Hare that he mustn't look at what she's going to make. He sees a silhouette of a crane through the window on the door, bursts in and sees... Guu making more shaved ice.
An episode of Pokémon has the ghost of a beautiful woman seducing James and Brock. This gets awkward when the ghost turns out to be a Gastly.
Not as awkward as you'd think — it turns out in the end that the Gastly's in it to propagate the REAL ghost's legend, and to make a little money on the side (it even materializes a cash register as it's talking to said real ghost; how does it make money, you ask? It disguises itself as a crazy old lady and sells fake wards and charms).
Also, the Gastly in question is MALE.
In the episode, "Just Waiting on a Friend", a Ninetales takes the form of a woman to lure Brock to her mansion because of mistaken identify. She had thought that Brock was her long-lost master. Given that the Ninetales 'are'' Kitsunes, it's surprising how long it took them to reference this trope.
Hana's boyfriend in Wolf Children Ame And Yuki reveals himself to be a wolf-man after they'd been going out for some time. His role is tragically cut short when he drowns in a storm drain while hunting.
An issue of Ninja High School features this almost exactly; Jeremy, visiting his grandfather in Japan, aids an injured crane, and a girl shows up to reside with them. Of course, she pays them back by working as a software programmer. In crane form.
The Good Neighbors has two swan maidens - well, one maiden and her brother - among the many, many fae in the college town at the center of the book. The whole folk tale is rather deconstructed, as when their skins are taken by a mortal, the girl is effectively forced into sexual slavery, and it's up to her brother to kill her and end her torment, as he can't act against her captor either.
In The Sandman novella Dream Hunters, a fox falls in love with a monk. Their love is doomed, though not for the usual reasons this sort of affair doesn't work out.
In the Brave / HowToTrainYourDragon crossover The Lady of The Loch Elinor is a selkie that was saved from the dragon Mor'du by Fergus, with whom she stayed with out of love and gratitude. Neither Fergus or her children are aware of this, which causes problems when the witch asks Merida to give her her mother's seal skin...
"Lover's Vow", one of the stories in Tales from the Darkside: The Movie, referenced this folklore trope. A gargoyle came to life and rescued a man from muggers, exacting a promise never to tell anyone what had happened. Later, the gargoyle appeared to him as a beautiful woman, whom he married and had two children with. When he broke the promise to her (he didn't know who she was), she and both the children transformed back into gargoyles in a very horrific process and killed him.
Although there is no shapeshifting involved, this is probably taken from the tale of the yuki-onna, where she first makes the man promise that he will never tell anyone of their meeting, and later marries him without his recognising her. The gruesome ending doesn't occur, though.
The 1964 Japanese ghost story anthology Kwaidan tells the yuki-onna story.
Green Snake, based on a Chinese folk tale, involves a serpent-spirit who seduces a young man by posing as a beautiful maiden.
Folklore and Mythology
The Pink Dolphin of the Amazon is thought to take human form at night, whereupon it seduces young, impressionable girls with its charm and impregnates them, returning to the river by the morning. Typically, when a girl in that region turns up pregnant and the father is unknown, fatherhood is attributed to the dolphin. A striking feature is that its blowhole remains even when the dolphin is in human form, which demands that it use a hat to conceal it when on land. Another identifying feature is that the dolphin people wear white while on land, and the dolphin-fathered children tend have dolphin-colored skin.
There is an Inuit legend about a petrel who is in love with a beautiful maiden, and transforms himself into a man so that he may marry her; however, his eyes are still those of a petrel and so he wears snow goggles to hide them. When the maiden takes them off, she sees his eyes and the spell is broken.
Swan Maidens - Common to mainland Europe, and Russia. The women (occasionally men too) in question are normally swans, but they leave their feathered cloaks behind when they bathe as humans. This has influenced many stories, modern and old including the ballet Swan Lake, Swanmays in Three Hearts and Three Lions and Dungeons & Dragons, Anita Blake's Swan Men, etc.
Selkies - Celtic and Nordic legendary seal people. If a man captures a female Selkie's skin, she is in his power and must be his wife, but she will return to the sea as soon as she finds her seal skin. In some versions of the story, the children follow their mother and transform into seals, or alternatively, drown. In others, most famously the film "The Secret of the Roan Inish", the children cannot change as they are (mostly) normal humans and are left behind (and confused unless their father explains what happened). The male Selkies are seducers of women. There is a similar American Indian story of a seal boy. This again crops up often in modern fiction and other works, and has also inspired a Dungeons and Dragons race.
Melusine - There are many versions of this romantic French tale. In one version, Melusine fell in love with a human and appeared to him as a beautiful woman. When they were married, she made her husband promise that she would have some time to herself each week. Wouldn't you know it, one day he breaks his promise and sees that she is actually a dragon (depending on other variants, she's even half-snake). Melusine is forced to go back to her family, but her children stay with the humans and a group of French nobility claimed to be her descendants for many years.
"Hans My Hedgehog" is yet another variant. It is probably best known for being dramatized in an episode of the cult favorite Jim Henson series, The Storyteller.
In "The Myrtle", a woman wishes for a child, even a sprig of myrtle, and gives birth to one. A prince is so enthralled by it that he buys it from her, and the myrtle changes to a Fairy in his rooms at night.
In "The She-Wolf", the bride was a wolf, with a wolfskin, before the miller's son nailed it down so it would not fly back to her; then, later, her son tells her where to find it.
In the variants of the Chivalric RomanceThe Swan Children, the bride is more or less clearly a swan-maiden; she gives birth to children who are first exposed and then transformed into swans by removing the chains they wear about their necks. When this is discovered, the children are changed back by restoring —except that one chain was melted down, trapping that child in swan form.
Tennyo (Heavenly Maidens) - Japanese imports of Indian and Chinese Buddhist figures. The males are called Tennin. They don't change from animals but they do need a feathered garment (a hagoromo) to fly back to the heavens. The Noh play Hagoromo features the core story where the the garment in question is stolen.
Kitsune (fox-spirits) and Tanuki (raccoon dog spirits) - Japanese trickster animal spirits. They don't leave skins behind, but they sometimes transform into beautiful women and marry men. They must leave if the man discovers their identity. Sometimes they are malicious and sometimes they are kindly. They are also sometimes female as humans, but male in their true animal forms.
Not just male; among the best-known traits of the Tanuki are its ridiculously large testicles.
That's nothin'. On occasion it's implied that both sexes have the testicles, which, as far as fantastical creatures go, makes a certain amount of sense (dwarf beards, anyone?), but considering the tanuki is also a real animal is just plain weird.
The strong vulpine predisposition to womanhood is also by no means binding; they are known often to have impersonated men, although a lower percentage of these are for romantic purposes.
On that note, there is a myth of an idiot who gets a cute young fox drunk and lets it snuggle up next to him for the night. When he wakes up, he finds a naked boy next to him right when his parents look in.
The recognized psychological condition of being kitsunetsuki, thinking you're possessed by a fox, is pretty much the Japanese version of clinical lycanthropy, but spent a very long time as a general diagnosis for crazy people. A lord once sent a very sharply worded letter to the god Inari for the inconvenience a possessing fox caused his household. True story.
One particularly famous positively-depicted Fox Wife is Kuzunoha, mother of the Japanese Merlin. (A guy with the bonus cred of actually having existed.)
Gumiho are the Korean version of the nine-tailed fox. They occasionally seduce men, though normally they're trying to win his heart (or liver) in a more literal sense.
Toyotama-hime (also known as Oto-hime) - Her story is remarkably similar to that of Melusine's. Once again, she was a dragoness, specifically, the daughter of Ryujin, the Dragon King of Japan, and fell in love with the fisherman Urashima Taro. And as always, it didn't end well for them. Note that she has had at least one (slightly more) successful relationship, albeit with the god Hoori.
The Crane Wife. A poor man finds an injured crane, and nurses it back to health. It flies away, and soon a beautiful woman shows up and marries him. She helps make him wealthy with her weaving, with the condition that he never watch her weave. He gets greedy and breaks this rule, and sees her in Crane form weaving her feathers into the silk. She then leaves once her identity is discovered.
A Japanese story featuring a yuki-onna followed Melusine's path in a way. A man got lost in a blizzard and this snow woman showed him the way out: she made him promise never to speak of the encounter to anyone or she would kill him. Later this man meets a beautiful woman and marries her. Many years, and a son, follow and one night, after a bit of sake, the man tells his wife of the yuki-onna. The wife stands up and reveals herself to be the yuki-onna, immensely annoyed, and leaves but does not kill him. It varies on whether her reason for sparing his life was that she had given him a son and hence had some sort of emotional attachment or that since he hadn't technically told anyone else.
Second husband of Inuit sea godness, Sedna turned out to be a petrel-spirit in disguise. In some myths it’s the reason she left him later. Other Inuit legends claim that in the The Time of Myths it was normal for spirits to cross border between human and animal world and vice versa. Many of them are love stories.
The Arabian Nights features the story of Janshah's pursuit of Shamsah. She was a Djinn who also turned into a swan by using a feathered cloak. She managed to ferret out that her swan-cloak was buried under her (new) palace the minute her fiance buried it.
A somewhat modified version of this story appears in Lotte Reineger's The Adventures of Prince Achmed. Peri Banu, a Fairy woman who uses a feathered gown to fly around as a bird, isn't too upset when the prince proposes to her, though.
The book The Sterkarm Handshake features no actual swan-mays, but the Shapeshifting Lover legend does feature heavily in the story. The main female character, Andrea, is part of a group of time travellers from Twenty Minutes into the Future who travel to medieval times. When in the past, the time travellers say that they are elves. Andrea falls in love with a man from the past, but he is wary of entering into a relationship with her because swan-mays, as he thinks Andrea is, always leave their human lovers eventually. (Guess what happens at the end.)
Megan Whalen Turner referenced the Selkie legend in one of the short stories in her book "Instead Of Three Wishes". In the story, a Selkie who has been searching for her coat for many years enlists a young girl to help her find it, after the man who tried to force her to marry him hid her coat in a painting.
In the dark fantasy novel, The Folk Keeper, the heroine has an unusual affinity for the mysterious creatures of the title. Turns out she's a half-Selkie. She tries to escape in her seal-form by wearing her magical skin, but it had been too damaged by the villain, making it impossible to ever remove it. Not wanting to give up her human form permanently, she rips off the skin before it's too late and loses it in a storm. She may be separated from her family, but can still have a connection to the sea without the skin, and at least this way she can stay with the nice human guy who loves her.
Selkie Girl by Laurie Brooks is a retelling of this story. The main character Elin Jean has had webbed fingers her whole life. She finds out that her mom is a selkie. Elin then becomes a selkie as well.
In the Belgariad and prequels, Poledra is a variation, since she genuinely decided to be Belgarath's wife. She is capable of switching between forms at will and is evidently as immortal as Belgarath.
The novel The Woman Who Loved Reindeer is a rare gender-flipped version of the story. It is pretty much Exactly What It Says on the Tin. The woman of the title falls for a legendary being known as a "Trangle", essentially a reindeer that occasionally looks like a man and transforms by removing his deer skin. There is an interesting complication in the relationship in that the Trangle is extremely aloof and uncomfortable around humans, and it is implied near the end that he will show his lover how to transform into a reindeer herself so that their relationship can actually get anywhere.
Elizabeth Marshall Thomas' palaeolithic romance The Animal Wife is a realistic and anthropologically rationalised story about an incident the like of which might have given rise to the widespread "animal wife" folk-tale motif. Not that anyone in the story thinks the "wife" is a shape-changer, but you can see where the story would go once it was retold a few times.
Peter S. Beagle has a short story called "The Tale Of Junko And Sayuri", where a hunter wounds an otter and takes it home with him to nurse it back to health. Once the otter is healed, it transforms into a woman and becomes his wife, who uses her power to help him move up in life, all the time not knowing what exactly she is. It turns out she's an ushi-oni.
In the Old Norse Saga of Hrolf Kraki, the prince Bjorn is cursed by his Wicked Stepmother to transform into a bear. However, each night he turns back into a man and returns to his lover Bera.
In The House of Night series, Rephaim, a Raven-Mocker, is given the gift of humanity by Nyx. However, he can only be a human at night and is forced to turn back into a Raven-Mocker during the day. This causes problems in his relationship with Stevie Rae.
In Patricia A. McKillip's Solstice Wood, Owen recounts the story he had been told of a man who shot a deer without killing it and went to track it down, and found instead a woman with a bullet wound in her shoulder. She lived with him for a year and half and had a son before she vanished. Then he explains that he finally realized it was his parents.
The Swanmays of Dungeons & Dragons are a secretive all-female order of humanoid rangers and druids who can turn into swans.
Selkies are aquatic fey in Dungeons & Dragons and often travel among surface races for a time, sometimes dallying with the surfacers, but almost all eventually return to the sea.
Silver Dragons from Dungeons & Dragons, being one of the few dragons to both have the shapeshift ability and enjoy cohabitation with humanoid races, are sometimes known to do this multiple times across their very long lifespan.
Selkies are also one of the kiths in Changeling: The Dreaming. Their sealskin coat can take the form of any garment from a peacoat to a belt, and they wither and die (well, they forget all about fae existence until the next incarnation) if they spend too long away from the coast.
The basis of Iroha's Back Story in Samurai Shodown Tenka. During one of her super moves, during which she disrobes and attacks the opponent behind a screen, her silhouette briefly flickers into that of a crane's.
Subverted in Da Capo with Yoriko. She's a girl with cat ears, and is indeed a cat that transformed into a girl. However, she transformed into the form of her owner, and her owner was piloting the body. At the end when the tree dies, the girl's real body wakes up and transfers into his school, at which point they enter a real relationship.
The selkie legend appears in Hanna Is Not a Boy's Name, with a little bit of deconstruction: Mrs. Hatch is a selkie, and since Mr. Hatch stole her skin, she's been stuck as his human wife for nearly two decades. She hates her husband and her son, and looking for the skin got another character killed.
The Pink Dolphin legend shows up in The Wild Thornberrys, but with a girl who Eliza believes to be a shape shifting River Dolphin who wants to transform Debbie into a River Dolphin because she wants a friend and is lonely. Debbie doesn't transform but it is never confirmed whether the girl in question was a Dolphin or not. Knowing about the above story gives the episode a distinctive lesbian subtext.
In the Gargoyles episode "Mark of the Panther", Eliza's mother tells the story of Anansi and a panther. Anansi turned the panther into a human woman and threatened to leave her trapped in that form forever unless she built him a city and provided him food. The panther turned woman marries a wealthy man and together they build a city and raise a family. Anansi undoes his curse, but sets up the panther to be hunted and killed by her human son since he's unhappy about losing her offerings. At the last second the son recognizes his mother and he turns into a panther to be with her. Since this is Gargoyles, the story has a lot more truth than Eliza's mother realizes.