Mystery Cult

Popular in ancient Greece and Rome, Mystery Cults are ultra-exclusive 'clubs' that require total secrecy on the part of participants and may tell new members little or nothing about their ethos before they join, and often long after. Generally speaking only long-time members will know what the cult is actually about, and even then the 'Inner Circle' will be the only ones who know everything. In this respect they are the opposite of some religions such as Christianity, Islam, and Buddhism, which are more evangelical and make materials relating to their beliefs freely available and are happy to explain what they believe.

As a general rule initiates don't have a clue what they have gotten themselves into and the inner circle won't be keen on telling. This is often a lead in to a really obvious Religion of Evil. Compare and contrast Ancient Conspiracy.

Note: As a general rule this trope only applies to things that are described as a cult, religion, or sect, etc, In-Universe or by Word of God.

Examples of Mystery Cult include:

Literature

Skulduggery Pleasant features so many that they might as well be the entire premise.
Ngaio Marsh's Death In Ectasy features a cult in the mid 1930s. The murder victim is poisoned in the special beverage she drinks during a ritual. Naturally, the investigation is hampered a bit by the secrecy of the cult members.
The real-life cult of Mithras has featured in several historical novels, among them Rosemary Sutcliff's The Eagle of the Ninth and John M. Ford's The Dragon Waiting, which each have a protagonist who's a member.
In Elantris, the aptly-named Mysteries is an enigmatic cult with a very unpleasant (and largely deserved) reputation. Turns out that it's a corrupted knockoff of the peaceful Jesker religion, but where Jesker is dedicated to living in harmony with the Dor, the Mysteries is just about hacking into it to gain supernatural powers. King Iadon of Arelon is a follower of the Mysteries, and when he's caught in the middle of sacrificing a servant as part of a ritual, his already-shaky reign outright collapses.

Live Action TV

Battlestar Galactica: Mithras apparently has an analog in the Twelve Colonies of Man, but given that they're referred to as "Mithrasaries" it's possible they're not as secretive as the followers of Mithras on Earth. Apparently, old-school religious Gemenon considers them something of a protected minority.
Monotheism in Caprica is this by necessity: monotheism is illegal on Caprica.
"The Silence" in Doctor Who is portrayed as a Mystery Religion dedicated to stopping the asking of a Question - though really it is more of a Single-Precept Religion than anything.

Tabletop RPG

In Call of Cthulhu the cults that worship the Cthulhu Mythos deities are like this. They're intensely secretive because their abhorrent practices would get them imprisoned or executed in any civilized country. By the time a new member finds out what the cult is really up to they've probably been driven insane.
In Warhammer 40,000 the same often applies to Chaos cults. Genestealer "cults" internally are the opposite due to their hive-minded nature, but their main modus operandi is hijacking and/or mimicry of other sorts of cults (whatever locals consider acceptable), which will fit the trope as a consequence.
Shar, one of the major deities in the Forgotten Realms, is usually worshiped by secret cults instead of large public temples, being the goddess of Darkness, Secrets, and Forgetfulness. And the colors of her priests are black and purple. And theocracies, of course, usually have any banned faction adopt facade of some approved (or at least tolerated) type of activities.
The Secret Societies in Paranoia play with this trope to various degrees, with the Illuminati being the textbook example. Members know almost nothing about the group, and typically their only contact are random visits in the middle of the night by a single masked stranger delivering inexplicable orders.

Western Animation

Futurama: The league of robots - a secret society of well-to-do wealthy robots (that somehow ends up having Bender as a member), that ostensibly exists to mastermind the robot dream of killing all humans, but in actuality, turns out to be more like a stagnant gentleman's social club.

Real Life

In general, any cult or religious organization that structures itself in this way can be considered an esoteric body.
The Mithraic Mysteries was a cult dating to about the first-fourth centuries. Because of their mysterious nature we know almost nothing about them, beyond that they believed their god emerged from a lump of solid stone as a fully formed adult. Other than that it's pretty vague. A popular myth rose up about hundred years ago in connection with the cult which says that Christianity was based on it. The short answer is that it was very definitely not.
The best known historical example were the Eleusinian Mysteries, which is believed to have been a Demeter cult that had the story of Persephone at its center as an explanation for the passing of seasons and possibly a cyclic nature of life.
- There are also records of a cult of Isis in Ancient Greece.
The best-known modern example would be the Freemasons, a loose fraternal association of secret societies which conduct their own private rituals.