Multiple-Tailed Beast

Normally in nature no creature has more than one tail. Not so in fiction.

Any creature at all can have more than one tail, often to establish its other-worldliness. Sometimes the tails look like they might come from different creatures entirely. Usually such a creature is some form of supernatural or semi-divine spirit being, elemental or demon. Youkai especially are known for having multiple tails, the most famous of which that does is the Kitsune, which is depicted with up to nine tails. The Nekomata is another commonly portrayed multi-tailed youkai, which has the appearance of a two-tailed cat.

This trope comes in two main forms:

A Split Tail: in which the creature has what appears to be a single tail starting from the base of its spine but it splits partway along into two or more tips.
Full Multiple Tails: in which the creature has more than one complete tail springing directly from the base of its spine.

Compare Kitsune, most instances of which will fall under this trope. Doesn't have anything to do with Twin Tails.

A very rare Truth in Television: sometimes animals are born with extra limbs, tails included. For example, here's a twin-tailed cat found in Canada.

Not to be confused with the Beast with Two Backs.

Examples of Multiple-Tailed Beast include:

Anime and Manga

Kuro the demon cat from Blue Exorcist has two tails of the split version.
In Naruto, Naruto and a few others are the containers for various multi-tailed animals.
Moro, the female Wolf God that raised San in Princess Mononoke had a two-pronged split-tail.
Yami to Boushi to Hon no Tabibito stars two kitsunes, one with nine tails and one with just three.

Film

King Ghidorah, who appears in several Godzilla movies. He has two long tails.
The Zipplebacks from How to Train Your Dragon.

Literature

The Harry Potter universe has (as mentioned in Fantastic Beasts and Where to Find Them) the Crup, which resembles a Jacky Russel apart from its forked tail. They normally have the ends clipped in order to preserve The Masquerade.
"Scraps", the Frankenstein's Monster of a Big Friendly Dog created by Igor in Carpe Jugulum.

Nanny Ogg: He's as happy as a dog with two ... oh, he does have two tails.

In The Dragonriders of Pern series Pernese dragons have forked tails.
"How To Draw" books that involve Anthros or Fantasy usually have a section that mentions this.

Live-Action TV

Korean drama My Girlfriend Is a Nine-Tailed Fox, in which case the eponymous girlfriend is a magical nine-tailed fox spirit taking human form.

Oral Tradition, Folklore, Myth and Legend

The Seth Animal, the creature that the Egyptian god Seth is supposed to have the head of, has a forked tail.
Aside from the nekomata and Kitsune, there are other Youkai with multiple tails. The Isonade is a giant shark with three tails (one larger and barbed), the Orochi is a Giant serpent with eight heads and sometimes eight tails, and the Raiju, or Thunderbeast, is depicted as various animals, sometimes described with multiple tails.

Tabletop Games

Dungeons & Dragons. The demon lord Demogorgon has two tails. The Warped Beasts also have multiple, flail-like tails.

Web Comics

While mutated rather then supernatural, the Hell Hound Action Girl Surama from Wurr has two tails.
In El Goonish Shive, Grace's omega form is a three-tailed squirrel-girl.

Video Games

Many species in Pokémon have multiple tails, such as Vulpix (six), Ninetales (obvious), and Tauros (three). Espeon has a forked tail with two tips, as do Uxie, Mesprit, and Azelf. Buizel and Floatzel have two (they even use them as propellers), as well as Ambipom, Purugly, and Electivire. There are also some ambiguous cases such as Grovyle (which has branching fern leaves for a tail) and Suicune (which has two ribbons for a tail).
Miles "Tails" Prower in the Sonic the Hedgehog series has two tails, and frequently uses them to helicopter around.
In the video games of Harry Potter, there are several references to the Gytrash, which are ghostly dogs with forked tails. The gytrash is a creature in English folklore, though only the Harry Potter games describe it with a forked tail.
Touhou, with its focus on youkai, unsurprisingly has this. There are Ran, a nine-tailed Kitsune, Chen, a twin-tailed nekomata, and, somewhat oddly, Orin, a kasha, who looks just like a nekomata despite the fact that they're mythologically unrelated.