Anonymous Author

An author who doesn't want their authorship known will use a Pen Name. An author who wants everyone to know they don't want their authorship known will use Anonymous, or a pen name that very obviously presents itself as a pen name.

This is done to convey the impression—which may even be true—that the author would be in trouble were his or her identity known. So it's often done with controversial works, or works that wish to present themselves as such, and with exposes.

Compare Pen Name. Contrast Same Face, Different Name, where the pseudonym may not even be particularly opaque and serves largely to emphasize Genre Adultery.

Examples of Anonymous Author include:

Fan Works

Unlike other fandom sites, Archive of Our Own permits authors to publish their fic anonymously, and even have an official collection (and several unofficial ones) to group them. This is to not confuse with the practice of orphaning, where the author deletes their profile and disavows their works, making then functionally anonymous for people who find them after the original author abandoned them.

Literature

2048, a singularly Anvilicious dystopian novel that could best be described as Nineteen Eighty-Four meets The Handmaid's Tale only much, much worse, attributed to Erica Blair.
Primary Colors by Anonymous. Fifteen years later, O by Anonymous.
- Also by Anonymous A Book With No Name.
Go Ask Alice... allegedly.
The Bride Stripped Bare. Australian Nikki Gemmell eventually revealed her authorship.
The Name Of This Book Is Secret and its sequels by Pseudonymous Bosch.
Frankenstein, on its initial publication, to hide that the author was a young woman.
During her lifetime, Jane Austen's novels only identified the author with the words "By a Lady".

Live-Action TV

Parodying Austen, The Two Ronnies serial 'The Phantom Raspberry Blower of Old London Town' was credited to 'Spike Milligan & A Gentleman' (The Gentleman being Ronnie Barker).

Theatre

A Prussian nobleman wrote plays under the name J.E. Mand -- jemand is German for "someone."

Video Games

Executive Meddling makes this a recurring issue in the games industry, where this often occurs involuntarily.
- In the 1970's and early 1980's American games industry, many companies refused to do credits as a means to prevent poaching. The website for the Atari brand has a blog post about this practice here.
- Many Japanese companies of the 1980's also refused to allow credits, also to prevent poaching, but Up to Eleven. A Time Extension article notes that the identities of the developers were considered company secrets.
- Still happens as of The New Twenties, amplified that many games are patchable digital downloads, not permanently etched in ROM. As a result, corporations sometimes publish versions of games with employee names absent if they leave for another company, as noted by this IGN article
Nearly all creators of the Visual Novel Katawa Shoujo use nicknames (e.g. cpl_crud, silentcook, Aura)
Many of the credits in Mega Man II are aliases, e.g. Inafking, Tom Pon, 2m03cm Man, Yuukichan's Papa, Fish Man)

Web Comics

The Wotch by Anne Onymous.