Sir, from The Miserable Mill, always has his face obscured by a massive cloud of cigar smoke.
In the original version and first adaptation of The Lorax, the Once-ler's face is never seen in either the "present" or "past" timeline. The second adaptation takes a different approach—see the Western Animation folder.
Discworld - Skazz, a student from the Unseen University has long hair that covers all of his face but his nose's tip.
Orual of C. S. Lewis's Till We Have Faces begins wearing a veil shortly before she becomes queen. As a result, her face becomes the subject of much rumor among the populace, and Orual herself was regarded as "something mysterious and awful". The truth of the matter is, she was ugly.
'She-Who-Must-Be-Obeyed' from H. Rider Haggard's She is usually draped from head to foot in gauzy, mummy-like wrappings because, according to her, her beauty drives men mad. Given that she is all-powerful men who do glimpse her are wise to meet her expectation.
Erik, the titular Phantom of The Phantom of the Opera, originally wore a full-face mask and was very much a Faceless - until subsequent remakes cut said mask and the underlying deformity down by a lot. A made-for-tv miniseries of this from the 90s goes a step further with this and never shows the Phantom's face to the audience, even when unmasked—thus rather neatly avoiding a possible Special Effects Failure.
Nathaniel Hawthorne's short story The Minister's Black Veil tells of a Puritan minister who one day inexplicably dons a black veil to cover his entire face. The simple addition of the veil changes him from a beloved and respected figure to an item of fear and horror, and he wears it for the rest of his life.
The face of Haliax, the Big Bad from The Name of the Wind (as well as most of the rest of him) is shrouded by both a black cloak and shadows. Considering the face of one of his subordinates that we do see, this is probably a good thing.
In James Swallow's Warhammer 40,000Red Fury, the Angels Sanguine wear their face-concealing helmets even among their fellow Space Marines, also sons of Sanguinius; they only take them off when among themselves, and even there, they wear face shadowing hoods.
The Reaper from Elfstones of Shannara. (And for that matter, for much of his appearances, the Dagda Mor, too.)
Squickily literal example from the Dragonlance Taladas Trilogy- Big Bad Maladar peeled his face off as part of an unknown dark ritual, leaving a skull-like ruin behind. Even he's rather ashamed of this, so he usually wears a deep hood with magical shadow inside it to conceal his deformity, revealing it only when he wants to strike terror. This habit actually earned him the nickname "the Faceless Emperor" in-universe.
In Moon Over Soho the Big Bad uses magic to make his face look blank, and if you pierce the magic spell he has a full face mask, to conceal his identity.
In the original picture book of Mars Needs Moms, Mom's face isn't shown until the end when she gives her space helmet to her son so he won't suffocate, almost dying in the process.
Many, though not all, of the Ten Who Were Taken from the Black Company novels are fond of hiding their faces- one of them takes this to the point that he's actually known as the Faceless Man (all the Taken, like most wizards in this setting, go by descriptive titles, since their true names could hold power over them). Most prominent, however, is Soulcatcher, who keeps her face concealed behind her helmet for the entire first novel- in fact, between the face-hiding and the fact that she usually wears masculine clothing, it's not until the end of the book that the protagonists are even sure she's female.
Chlorr from the Old Kingdom trilogy is known as Chlorr of the Mask for a reason; she always hides her face behind a bronze mask and continues to do so even after becoming a Greater Dead, meaning that her original mortal features would have largely ceased to exist. Later on, Mogget taunts her by calling her "Chlorr No-Face", implying that there may be a very good reason for the mask. The prequel Clariel, Chlorr's Start of Darkness, reveals that the original purpose of the mask was to provide protection from Free Magic creatures that can burn human skin with a touch; by the novel's end, Clariel's/Chlorr's face has been burned and she's using the mask to cover it up.
"The Voice in the Tunnel", a mysterious cat that Ivypool and Blossomfall encounter in Sign of the Moon is one. Because it's really, really dark in the tunnel, and because Ivypool apparently can't tell voices apart, Ivypool can't make out any of their features, nor can she figure out their gender. It wasn't until the following book, The Forgotten Warrior, that Ivypool returns to the tunnel and meets up with this character again that she finds out who they are. It's Hollyleaf, a vanished and presumed dead protagonist from the previous story arc, Power of Three. Just as suspected by fans.
Also in The Forgotten Warrior, the prologue begins with a mysterious cat that is not described and is referred to with only gender neutral pronouns. Speculation went wild when the prologue was released online. The final verdict on the mystery: Although the prologue is made to make you think it's Hollyleaf, it's definitely not her. We never do find out who it is, but given the events of the novel it is almost certainly Sol.
Big BadGerridon from the Chronicles of the Kencyrath has never had his face clearly glimpsed or described in any of the novels - he's always shrouded in shadow/ wearing a mask/ standing behind the POV character or an object/ etc. Heroine Jame actually lampshades this fact in Sea of Time, thinking to herself that it's ironic that despite the fact that Gerridon's influence has shaped her life, she's never actually gotten a good look at his face.
Ser Robert Strong in A Song of Ice and Fire, he is a massive towering knight, completely clad in armor, and no one knows who he really is or what he looks like. There are theories that he is Gregor Clegane resurrected by Qyburn.
Avshar, Big Bad of the Videssos Cycle, always wears some configuration of helmet, hood, and/or veil in his on-page appearances, revealing his true face only when he wishes to strike terror. The reader finally finds out what he looks like in the last book when he unmasks himself in front of the protagonists - the centuries-old Avshar suffers from Age Without Youth (at least in appearance - he has the strength and vitality of a man in his prime) and now resembles a mummified corpse more than a living man. This neatly explains why Avshar prefers to conceal his appearance, and why the revelation of it invariably results in a horrified reaction.
In The Year of Rogue Dragons, the wizard Scattercloak always wears a hooded cloak, veil and gloves, and never takes them off even at meals (he'll sit at the table, but he goes somewhere private to actually eat). He even masks his voice, speaking in an androgynous, accentless, possibly synthetic monotone. It's never revealed why he does it—it could all be pure affectation for all anyone knows.
Terian, Tobimar's patron god, is always depicted with his face concealed by a blaze of light.
Myrionar, Kyri's patron god, takes it a whole lot further: As the god of justice, for all people regardless of race, gender, or category, It is referred to with a gender-neutral pronoun and never shows Its face nor allows Its face to be depicted, so that Its own categories (if it has them) are not apparent. It is always represented by Its emblem, a set of scales balanced on a sword tip.