Doctor Doom, enemy of the Fantastic Four, another deformed-beneath-the-mask type. Doom may be one of the longest-running examples of this trope; Marvel has enforced an ironclad "Doom's face is never shown!" rule for over fifty years. Characters who do see his face are almost invariably filled with a mix of extreme disgust and abject terror.
Doom's face before the accident that deformed him is sometimes shown in Flashbacks. There's also Secret Wars, where his face is (temporarily) fixed.
Mary Jane Watson from the Spider-Man comics has her face obscured in her first few appearances before becoming the main love interest.
This also had the effect that, since we never saw her face, and Peter was continually avoiding being set up with her on the assumption she wasn't attractive, the readers had the same surprise as him when he answered the door to her in a Splash Panel.
The Green Goblin in his first appearances was always either wearing his mask or had his face obscured by some random object.
Subverted with Judge Death. At first, he is built up as an Evil Counterpart to Dredd complete with a warped version of his Iconic Outfit. In his Origin Story, he is shown as a human being sans helmet and how he became an undead monster.
Judge Fear: we never see his true face, just his helmet, which covers all his face and which he can open, which is apparently so frightening it can scare people to death — gaze into the face of fear! Does not always work: Dredd: gaze into the fist of Dredd!
V in V for Vendetta chooses to remain behind his mask for the entire duration of the narrative, save for his revealing himself to Dr. Delia Surridge as she lays dying. She comments that his hideously burn-scarred face is "so beautiful..." This trope exists partly because V is more embodied as an Idea than as Individual.
In the film adaptation (so goes the story), various prettyboy types were considered for the role of V, but they all wanted to do at least one scene unmasked. Hugo Weaving was therefore enlisted instead and his mask is never removed. The "mystery factor" is diminished since Weaving looks pretty much the same ineverymovie, but what was lost there is regained in spades in the voice and physical acting. He does get a cameo in that he's one of the prominent faces (along with the others are characters who have died in the course of the film) in the crowd removing their masks at the end. It's rather poignant.
Preacher - John Wayne acted as a spirit guide to Jesse Custer. His face was always in shadow, even in the middle of Monument Valley with no shade. A similar thing occurs with the mysterious fat guy that Jesse gives a lift to in issue #53.
An X-Files comic about the Fatima Prophecies had a scene with the Pope and a military commander discussing the third (unopened) prophecy. There were no backgrounds or faces, just the two symbolic outfits of "military" and "church".
Taskmaster from Marvel Comics does better than most costumed types at concealing his true name and face; he never takes off his mask in-panel, whether others are around or not. When he is defeated and his mask is stolen in his own miniseries, we see him only in silhouette, and then from behind, before he retrieves his mask and makes sure the ones who took it aren't going to be telling anyone.
One of the Udon comics actually did show him without the mask on... in a flashback to when he was twelve or so.
Goes so far that when he's working with Deadpool and wearing a copy of his costume, he can be seen wearing his traditional skull mask underneath his Deadpool mask.
It was shown once when Moon Knight defeated him and threatened to cut off his face literally but instead decided to just cut his mask off.
Subverted in Radioactive Man by one of the members of "The Hellfire Club", sitting in shadow an profile, one of whom is clearly Richard Nixon:
"Gee, it sure is dark in here. You'd think with all our power and money we could afford a few lightbulbs."
In The DCU, JSA villain Johnny Sorrow no longer has a face, and to look into the space behind his mask where his face should be is instant death.
This is one of the trademarks of The Phantom (Ghost Who Walks, Man Who Cannot Die, etc.). When in costume he has his mask, and when travelling incognito as "Mr. Walker" he wears a hat and sunglasses all the time, claiming that he has a disfiguring skin condition when asked to remove them. If he isn't wearing the mask or the hat and glasses for some reason, he's either drawn from the back or in shadow to obscure his face.
Flaming Carrot - Carrot's identity is kept a mystery to the reader, and the only time we see him without his mask is when his face is covered in bandages. According to some theories, he's actually Jim Morrison.
In Zot!, the electronic assassin 9-Jack-9 has no face. (Creating difficulty for creator Scott McCloud when he held a contest for which character the readers most wanted to see hit in the face with a pie, and 9-Jack-9 won. It ended up passing through him and hitting Zot, the runner-up, instead.)
Variation: Usagi Yojimbo's Big Bad, Lord Hijiki, is one of these—but only after his face is completely shown in his first appearance.
Arch-villain The Octopus in The Spirit is only ever seen as a hand or pair of hands wearing distinctive gloves.
Monsieur Choc, the arch-villain in Tif Et Tondu is never seen without a knight's helmet that completely disguises his features. In the two page comic L'Image de Choc one character eventually get hold of a picture of Choc without his helmet. However, the picture turns out to be useless Since it depicts Choc when he was an infant.
The Phantom Stranger from The DCU manages to keep the top of his face permanently obscured in shadow (thanks to carefully angling his hat) to the point that it seems like he wears a Domino Mask.
Both incarnations of Marvel Comics' Baron Zemo have had their masks literally fused to their face. The younger Baron eventually finds a way to remove his, but his face is horribly scarred underneath.
In the Batman storyline No Man's Land, the person who takes the identity of Batgirl is never shown without her mask until Batman fires her, at which point she's revealed to be Huntress.
Legion of Super-Heroes villain Mano wore a transparent bubble helmet filled with the poisonous gases he needed to breathe so all the reader ever saw was a shadowy silhouette of his head.
Another example from the Legion: the Time Trapper. His face is always in shadow from the hood of his tattered purple robe. In the recent Final Crisis: Legion of Three Worlds miniseries, he was revealed to be A future version of Superboy Prime.
Mind you the Time Trapper has had his/her/its identity revealed four or five times making the TT effectively faceless no matter what. In LO3W, Brainiac 5 speculates that the Trapper is a living alternate future, whose history is constantly rewritten (he/she's previously been a Controller, his/her own sidekick Glorith, a future version of Cosmic Boy, the Anthropomorphic Personification of Entropy, and a future version of Lori Morning [who may have been the Post-Crisis Glorith]).
Ferro Lad is basically a heroic Dr Doom with transformation powers.
The Punisher MAX - Subverted and averted with Finn Cooley. An Irish bomb-maker, his face was blown off, so he was grotesque and disfigured, and his face was shown frequently during the "Kitchen Irish" storyline.
In American Born Chinese, Jin and Danny's parents always have their faces partially or completely hidden. Subverted when Danny's parents are finally shown, revealing that Danny's parents are Jin's parents (since Danny and Jin are the same person).
In Superman comics, Tiny Bubbles, a superstrong Intergang enforcer had her face constantly obscured (from the reader, but not from other characters). When a reader wrote to the editor to ask about this, they said it just seemed like a fun idea.
From Dork Tower: Leslie, Bill's (sole) employee at Pegasaurus Games, is always shown with her face half-hidden behind the store counter.
Chick Tracts often portray God as an enormous throned figure whose face is silhouetted by light, making him look eerily like The Blank.
In Mickey Mouse Outwits The Phantom Blot by Floyd Gottfredson, Mickey Mouse meets the Phantom Blot for the first time and, well, outwits him, so he is unmasked at the end, showing him to have a striking resemblance to Walt Disney. However, later appearances in American Disney comics (often drawn by Paul Murry) never showed The Blot's face. He would sometimes wear masks that looked exactly like a human face on top of his black hood... but we are even told on-panel in one comic that no one has ever seen his face (which is weird, since he regularly ends in jail - shouldn't they remove his hood then?). In European Disney comics, however, the unmasking was canon, and he regularly appeared without his hood - after all, it made him less conspicuous to the public.
It gets weirder: Egmont, the standard Disney publisher in northern europe, decided to make both, the unmasked Phantom and the never unmasked one, separate characters, often changing details when translating italian comics to do so. The unmasked version is named "Plattnase" (Flatnose) and often doesn't were the hood in the whole story while the masked version is called "Schwarzes Phantom" (Black Phantom)and Mickey sometimes doubts that he is even human (well, the local equivalent of human). Recently, they have become the same character again, though.
In Le Scorpion, Captain Rochnan's face is not revealed until The Treasure of the Templars; his face being concealed by his armoured helmet before this. And he falls to death not long after the reveal.
The Surgeon General from Give Me Liberty, whose face is always obscured by a surgical mask, cap, and tinted goggles.
Lampshaded in the Cracked parody of The Fall Guy. Colt asks Big Jack why she is suddenly wearing elaborate hats that conceal her face. Big Jack replies that the artist couldn't get her face right so decided to hide it behind the hat.
In Death Of The Family, The Joker's...face has not been shown. He has taken back his face-skin and is wearing it as a creepy mask. It's safe to say that his face is not a pretty sight.
In Paperinik New Adventures Camera 9's face (except for his beak) is always covered by his camera or (when it takes it off) by Scenery Censor. This was to enforce his belief that his job as cameraman (he was a very famous photografer once) transformed him in a mindless robot,since he thinks television is a shallow and loud way to reports news.
When Korinna was using the fake identity "Profunda",her face was always covered until The Reveal.
Rorschach from Comic Book/Watchman keeps his face hidden behind a shifting black-and-white mask, though he argues that that is his real face. He's not shy about taking it off during the day to walk around, spy on people in plain sight, and predict the end of the world.