Cryptid Episode

A Cryptid is an animal which is not yet known to modern science, such as Big Foot, Mothman, or the Loch Ness Monster. Sometimes, a show that is not usually focused on them will have an episode or two about them.

This type of episode can be used as a characterisation exercise, establishing some of the characters as believers and others as skeptics.

Possible plots for this kind of episode include:

The characters spend the episode trying to find the cryptid. In a Slice of Life series, they generally don't succeed, conclude that it must not exist, and go home. (Sometimes it will be revealed to the audience that the creature is Real After All, but the characters discovering a cryptid could permanently change their lives forever, and that's BAD).
The characters find a cryptid early in the episode, and spend the episode trying to look after it/hide it/help it find its way home.
Characters are traveling on holiday and encounter one. (Abominable Snowman seems to be the most common one for this, what with mountain getaways and Christmas Episodes providing plenty of snowy settings).
A show with a Monster of the Week format will have a cryptid as one of said monsters.
A crime show may come across a murder or other crime allegedly committed by a cryptid. The characters usually find out that there's a reasonable explanation for it.

If done clumsily, this can easily result in a BLAM Episode.

Examples of Cryptid Episode include:

Anime and Manga

Lupin III had an episode where Fujiko's singing voice attracted the Loch Ness Monster.
Creamy Mami, of all things, had an episode based around a sea monster.
In an episode of Sailor Moon, they find a sea monster while on vacation. It doesn't have any connection to the magic of the show.

Literature

In the short story "The Convenient Monster", The Saint uncovers a murder that looks like the work of the Loch Ness Monster. At the end of the story, the murderer is killed by the actual Loch Ness Monster.
Goosebumps uses either stock monsters (vampires, werewolves, mummies, etc.) or original ones, the sole exception being The Abominable Snowman of Pasadena.

Live Action TV

Heartbeat had one episode with the cops searching for some legendary big cats that were killing sheep on the Yorkshire moors. Turned out to be incompetent sheep rustlers instead.
iCarly has an episode centering around the hunt for Bigfoot.
MacGyver has an episode like this in the second or third season.
The infamous The Six Million Dollar Man episode where Steve Austin fights with Bigfoot.
- Spoofed on The Venture Brothers, where the show's version of Steve Austin is living with Bigfoot as lovers.
In one episode of The Dukes of Hazzard, The Greys are hiding in Hazzard County.
The Bones episode focusing on the Chupacabra cryptid uses it as a way to explore the difference in worldviews between rational, scientific female lead and her more open-minded male partner.
The Invisible Man (the Sci-Fi/USA TV series) did a Big Foot episode. Big Foot turns out to be naturally invisible. And a female.
The X-Files had enough cryptid episodes to stuff the Berlin Zoo full with them.
- And often subverted (and double subverted) them. A rampaging lake monster turns out to be a killer alligator while at the end the lake monster surfaces, unseen by anyone and a group of greys walking down a hill at an environmental spill turn out to be misidentification of men in Haz Mat suits.
Interestingly enough, Supernatural completely averts it: in the course of six-and-a-third seasons, the main characters have encountered angels, zombies and everything in between, but any hunter worth his rock salt knows that Bigfoot is a hoax.
How I Met Your Mother had a "cock-a-mouse," part cockroach, part mouse, capable of flight.
Harry and the Hendersons. Harry was Bigfoot.
Bigfoot and Wildboy. Bigfoot was, well, Bigfoot.

Puppet Shows

An episode of Gerry Anderson's Stingray has the submarine and crew shipped to Scotland to find the Loch Ness Monster.

Radio

One episode of The Navy Lark has the Troutbridge crew reassigned to find the Loch Ness Monster.

Web Original

Superpower Empire China 1912 deals with Alternate History but one of the episodes involves chasing a bigfoot in the Mongolian steppe.

Western Animation

The Lake Nose Monster from Phineas and Ferb.
One episode of Dexter's Laboratory featured Big Foot, while another used the Chupacabra.
One episode of Chowder has Chowder searching for Bigfood.
One episode of Garfield and Friends has Jon looking for Bigfeets.
In Godzilla the Animated Series, Godzilla fights the Loch Ness Monster.
In one episode, Angela Anaconda and her friends go looking for a yet- erm, sasquatch.
In one episode of Generator Rex, the creature he is fighting turns out not to be an EVO but is instead a (perfectly natural) chupacabra.
The "Little Bigfoot" episode of Sam and Max Freelance Police has Sam trying to rescue a young Bigfoot working as a busboy and return him to the wild. It turns out he wasn't a Bigfoot, just the son of a sideshow freak.
The Simpsons:
- In an attempt to become the world's most lovable billionaire, Mr. Burns goes to Loch Ness to capture Nessie.
- A sort-of example is the episode where Homer gets lost in the woods and is mistaken for Bigfoot.
A Monster of the Week in American Dragon: Jake Long was The Jersey Devil.
In the Futurama episode "Spanish Fry", Fry goes to look for Bigfoot, who appears at the end to act as a Deus Ex Machina.
In The Angry Beavers, Dagget meets "Big Byoo-tocks".
An episode of Gargoyles featured a visit to Loch Ness during the Avalon World Tour. Of course within the series, the Gargoyles themselves are technically cryptids too.