In many religious traditions, it is considered blasphemous to depict God visually. Whenever God is featured in a work of fiction, either His face is obscured or it's made explicit that His/Her chosen appearance is simply A Form You Are Comfortable With (the latter fulfills this trope conceptually if not directly). In Sunni Islam, it's also prohibited to depict the face of Mohammed, so in Islamic art he's frequently drawn as a figure with a face of pure light or something else of the sort. There are many old pieces of art that include the picture of Mohammed as well, but they have been defaced by later generations, and usually replaced his head with flames with similar symbolic meaning as the Christian halos.
In Christianity, it's not so much that it's blasphemous per se (otherwise,the Pope would have put the kibosh on Michaelangelo's renovation of the Sistene Chapel, especially the famed "Birth of Man that forms the centerpiece of the ceiling) to make representations of God, as much as it's well-nigh impossible to do it right — many artists throw up their hands in trying to put human limitations on a limitless being by trying to depict Him. That's why you either get the kindly man with a beard or... no depiction at all.
A National Geographic photo-essay about the White House staff had the president only shown from behind, with his face covered, or just out of frame. Not for secrecy, but because the focus of the article was his staff rather than him.
This is a pretty common practice whenever the president is featured in a tv show or movie, when they don't want to use a fictional president, but don't want to date themselves by portraying the one currently in office.
The Unknown Comic, who made a running gag out of performing with a paper bag over his head.
While American Professional Wrestling has portrayed masks as being Serious Business, Mexican lucha libre takes it very seriously. Once a luchador has donned a mask, he will never reveal his face in public again until he's beaten in a match where he put up his mask against that of another masked wreslter or an unmasked wrestler's hair as a bet to end a fued. If the Mask loses he takes off the mask and can never use it ever again, and if the Hair loses, he has to shave his head.
Ever heard of The Man in the Iron Mask? In real life the mask was made of silk, and the man was most likely a spy whose identity could have caused an international incident — not Louis XVI's identical twin as per the book and the movie.
During Saddam Hussein's trial, the presiding judge was always shown from behind.
Undercover police always wear masks on television to avoid being identified by criminals during operations.
This is standard depiction of Master P., also known as Anonymus, an unknown Hungarian writer from the 13th century.
In Britain (and maybe in other countries) during the era of steam railways, the ticket booths at railway stations commonly shielded the booking clerk from view of the public, for some reason - perhaps for privacy. This meant that the most you ever saw of the person who sold you your ticket was a disembodied hand in the hatch, and maybe they'd speak if you were really lucky.
In Brazil, the Silvio Santos Show had an announcer named Lombardi that was never seen by anyone. In fact, before the internet, no one even knew what he looked like. Even after his death, 90% of the audience of the program (that took almost all of Sunday's afternoons and evenings slots in that network) still doesn't know his face.
Also in Brazil, back in 2002, it was found out that a babysitter was abusing the children she was supposed to take care of. Enraged, the people of Aparecida de Goi‚nia lynched her. One such person, recorded on video, divekicked her in such a way that his legs made a perfect rhombus shape. He became a Memetic Badass known as Lindomar, the Brazilian Sub-Zero, but because he's seen from the back, the video quality was bad and his face appears for only a splitsecond, no one knows what he really looks like.
The dance crew Jabbawockeez wear white masks and white gloves in an attempt to invoke this, to avoid any one dancer from standing out over the crew as a whole during a performance.