A staple of "golden age" theatrical shorts (Looney Tunes, etc.) in the '40s and '50s was to have a human character, typically female, who was only shown from the knees down. Examples include Mammy Two-Shoes (and her white, sometimes Irish, replacement as seen in edited versions of the shorts and in the short-lived Tom and Jerry Tales), in the Tom and Jerry shorts; Sylvester and Tweety's owner in Tweetie Pie (though not Granny in the later shorts); J.L. in the Daffy Duck cartoon "The Scarlet Pumpernickel," and Marc Antony's owner in Chuck Jones' Feed the Kitty.
Parodied and/or homaged in both The Ren & Stimpy Show by Mr. and Mrs. Pipe, and in Cow and Chicken with the titular character's parents. In the latter even their shadows end at about the waist up.
Marvin the Martian in Looney Tunes, and by extension the entire Martian race as seen on Animaniacs (the episode "Clown and Out" ended with the Jerry Lewis-esque clown being blasted to Mars, where he's seen singing to Martian children) and ''Duck Dodgers', have this as a racial trait, their only physical facial feature being their eyes; otherwise, their face is a total blank.
The Big Bad of the sequel series The Legend of Korra, Amon, keeps his face hidden behind a mask. He claims his face was destroyed by the same Firebender who killed his family; it's a lie, although he is Crazy-Prepared enough to wear make-up that resembles a scar should he be forced to reveal his face.
Doctor Claw from the animated Inspector Gadget (who wasn't just faceless, he was mostly bodiless; only his arms and hands were ever shown). This was later ruined by a toy that did show his face and body (and utterly destroyed his coolness factor by presenting him as a skinny white-haired man with a twisted-lip sneer), and also to a somewhat lesser extent by a Super Nintendo game that showed half his face in the final battle (where he was at least given glowing eyes). The toy went out of its way to play it up, too. The packaging specifically covered his face with a sign, informing potential buyers that they would have to buy the package to see what he looked like.
Similarly, Spydra from Gadget Boy & Heather. The only time she takes off her mask on-screen (gleefully lampshading it in the process), she's polymorphed into Heather.
Miss Bellum on The Powerpuff Girls. Her full name is in fact Sara Bellum, homophonic to cerebellum, a tongue-in-cheek reference to the fact that her head is never displayed. And also a reference to the fact that she's really the brains at the Mayor's office. She gets a partial reveal in the 10th anniversary episode.
A minor character who fits is Mr. Morebucks, Princess' incredibly wealthy father who funds all her schemes. His face is never shown, and he also never talks on camera.
Kenny on South Park - with his full face finally shown in the movie South Park: Bigger, Longer & Uncut (and again on the season eight episode featuring Michael Ja—Jefferson.
In an early episode of íMucha Lucha!, Rikochet couldn't find his mask, and all they ever showed of him was really tight close ups of his eyes (and at one point, a shot where he's , and his head wearing other things (say, a paper bag, or a mailbox) to hide his masklessness. However, a model sheet of Rikochet's "special poses", which can be seen in the behind-the-scenes featurette on the "Heart of Lucha" DVD, shows four pictures of him without his mask, and all unobscured.
Nanny from Muppet Babies is usually only shown from the knees down.
It's because the babies are small and on the floor, and keeping them in the shot means only focusing on Nanny's legs. It turned into a Running Gag: if Nanny picks up a baby you still only see the back of her head or her chest from the neck down; pictures of Nanny have the faces obscured; and any other grownups who ever appear, such as a neighbouring friendly policeman, are shown the same way.
Cobra Commander, Destro, and Snake Eyes. Except Cobra Commander got revealed in the ill-received movie. Destro was subsequently shown without his mask via a 12" figure released in the mid-'90s (it was the main selling point!) and has since been shown without it in the current comics. Snake Eyes has been shown in one form of silhouette or another both pre- and post-scarring in all the various comics, usually showing the lower half of his face.
Eventually the comics gave Cobra Commander one as well, not nearly as cheesy as the movie's version. He just looked kind of like Che Guevara. Link. And even that was a disguise.
G.I. Joe: Renegades continues the tradition. We see only part of Cobra Commander's face. Destro is introduced prior to getting his mask but he gets it soon after, and Snake Eyes's remains mostly hidden, except for The Unreveal in one episode, when Zartan tried to steal his mask, and then promptly gave it back after commenting that Snake Eyes needed it more.
Subverted on the Cartoon Network original series Cow and Chicken: their parents are supposed to be faceless, but the first episode reveals they're actually no more than two pairs of legs.
The original shorts of The Fairly Oddparents had Timmy's Unnamed Parents are (like the ones from Cow and Chicken) never shown from the waist up, but when it was made into its own show the parents' faces were seen.
Subverted on Codename: Kids Next Door. The first episode with Numbuh One's father involves his father's face being obscured from view quite blatantly; midway through the episode, though, it's suddenly seen. Several of the other character's parents were The Faceless at first, but later were shown, though some of the parents still haven't been seen. During season 6, the mysterious kid from the KND Splinter Cell was only shown as a shadow. In the Finale, it was revealed that he was in fact Numbuh 74.239, and that the splinter cell was just a cover for the Galactic KND.
Number One, the main villain of Birdman, never removes his mask. (Then again, neither does Birdman himself.) For that matter, neither does Space Ghost. Nor Frankenstein Jr., who makes one wonder why the mask anyway - he's a Giant Robot — difficult to hide that without a mask!
Slade in Teen Titans, to such a degree that even getting a clear look at him in-costume (mask and all) is given the "big reveal" treatment. His mask is finally broken down the middle in the first season finale, but he manages to cover the other half of his face with one hand as he escapes. Later, during the fourth season finale, his mask is knocked off, but under extenuating circumstances: he's kinda-sorta dead, so all we get is a skull (although it was still a cool moment). The rationale appears to be that he is missing an eye — confirmed when his mask is removed during the fourth season finale.
Conrad Fleem in The Replacements is always shown from behind. His most distinguishing characteristic is a huge moustache.
In Darkwing Duck series, FOWL High Command is always shown in shadow, revealing nothing but shapes and eyes.
Batman-ish vigilante Nobody, from the second Teenage Mutant Ninja Turtles cartoon, is one of these when out of costume, with his face always covered in shadow—even when the lighting is such that it shouldn't.
Subverted in "Starcrossed" when they have to go into civilian disguise to hide in plain sight of the invading Thanagarians. Also made funny when Batman reveals that he's known who they all were the whole time.
Hawkgirl is a particularly interesting case, as her mask is part of a bulky, winged helmet, which she wears at all times, even when she's receiving medical attention inside Justice League headquarters. Her first unmasking, late in Season 2 (at the end of the second part of the episode "Wild Cards"), is presented as a dramatic and romantic scene. This is implied to be a point of Thanagarian culture—Hawkgirl stops wearing the mask/helmet for good after she severs ties with Thanagar.
The Question was this, until a tender unmasking scene with Huntress in the episode "Flashpoint". (Unlike the comic book version, who was seen unmasked regularly.)
Question: You were right. I am the ugliest guy of all time. Huntress: Not in my eyes.
Casey Jones is never seen without his mask on (unlike in all other versions, where he takes it off), even once when going undercover in a business suit.
Orko's people in Masters of the Universe keep their faces concealed under wide-brimmed hats and behind scarves; all that is visible are glowing yellow eyes in the shadows, and pointy blue ears sticking through the hat. It is explained in one episode of He-Man and the Masters of the Universe (1983) that showing one's face to another being is, in their culture, at a level of intimacy on par with getting engaged.
Dumb Donald's face in Fat Albert and the Cosby Kids is always hidden behind a pink stocking cap with eyeholes cut into it. The 2004 live-action film version (In which the series' main characters are sucked out of the television and into the real modern world) plays around with/lampshades his lack of facial features, as Donald eventually "gains" a face after the long stay in the real world starts to transform the animated characters into "real" people and unmasks. Once the gang re-enters their cartoon world, Donald's face "vanishes" and his "head" shown as just a pair of eyes before he puts his hat back on.
Secret Squirrel has the upper half of his face covered by a purple fedora hat with eyeholes cut into it.
His face was revealed once in "Goldflipper" while he was disguised as a girl scout.
In Cool McCool, Cool's boss Number One was only ever seen as arms and a cigar behind a chair.
Two years before Cool McCool was obscure Terrytoons character James Hound, whose superior was also behind a chair and never seen facewise.
Subverted in a couple of specials however, such as "Is This Goodbye, Charlie Brown?," where we do clearly see some adults. Also averted in the "This is America, Charlie Brown," miniseries from the late 80's, since it features many historical figures fully interacting with the main characters.
There's also "the cat next door,'' whose claw is the only feature seen by the audience when it regularly destroys Snoopy's doghouse.
Most of the character's parents in Tiny Toon Adventures are only shown from the waist down, the exceptions being Hampton's parents, Elmyra's parents, and Plucky's Dad's face has been seen a few times.
In Batman: The Brave and the Bold, Bruce Wayne is never seen without his mask. If he's not wearing it, he'll be in shadow until he is. Finally averted in "Chill In The Night", where he unmasks himself to Joe Chill, the man who killed Thomas and Martha Wayne, just to strike a whole other level of fear into the guy.
In Batman: The Animated Series, there's an episode, "P.O.V.", which features a very puzzling example of this trope. Batman and three of the Gotham Police Department's detectives work together (though they don't officially team up) to bring down a crime ring. The Big Bad in charge of the gang is always seen either in shadow or partially in shadow, so we can only see the outline of his face and some of his more notable facial features. He looks suspiciously like The Penguin (short and bespectacled), but obviously can't be because (if the basic shape of his face is any indication) he is not at all disfigured like the Penguin. What makes him an especially frustrating character is the fact that Batman apparently knows who he is, but he won't tell us! And as if all that weren't mysterious enough, this villain is The Voiceless as well!
In X-Men: Evolution, Magneto's almost always wears his helmet, as in most versions, but here the helmet's shadow often obscures his face as well, leaving only his eyes (which glow white when he's using or about to use his powers) visible. If Magento has the helmet on and the shadow isn't there, he's usually about to be given either a Pet the Dog or a moment of weakness- in other words, something that humanizes him. If the shadow's there, he'll usually be in straight villain mode. His face was revealed at the end of the first season, and from then on we see it even when he is wearing the helmet. Its implied that his earlier "appearances" were actually astral projection, and this Magneto appears to have telepathic powers, which is actually something he had in the comics that people seem to of forgotten about.
On the animated adaptation of The Ricky Gervais Show, Carl's longtime girlfriend Susanne is The Faceless, always shown from behind or her face hidden by a book, a lamp, or other object, if not cast completely in darkness.
Ms. Mimi in her first appearance Angelina Ballerina: The Next Steps. Her face is covered by the boxes she carries and is seen by the back of her head applauding for Angelina. Her face is revealed in the next episode.
Superman: The Animated Series (and its later spin-off Justice League Unlimited) features the Toyman, aka Winslow Schott. Orphaned after his father dies in prison, Toyman becomes a toy-crazed supervillain, hiding his face behind a Howdy Doody-like mask. Schott is never seen without the mask, although it's frequently cracked and broken in his battles with Superman, and even his fellow villains.
Tn the Mighty Man and Yukk! shorts on the Plastic Man Comedy/Adventure Show, Yukk! was supposedly the "world's ugliest dog." As such, he wore a miniature doghouse on his head that concealed his features. But whenever it became convenient to the plot to stun an adversary into terror-induced paralysis, Yukk! would lift his doghouse, and show them his face...At which point whoever was looking would absolutely freak out in gaggle-eyed horror. Of course, the audience only ever saw Yukk!'s head from behind in these instances.
The original three BIONICLE movies were very weird about this. All of the true faces of mask-wearing characters (all the Matoran, Toa, Turaga and Makuta) were kept a secret. Their heads were shown from all conceivable angles, bar from the front, so we got a vague idea of what they may look like, but the precise facial details were still a mystery. Interestingly, despite the director's apparent efforts, the entire head of Makutawas indeed visible through the electric flashes in the first movie, and it looked exactly like on his toy — a regular Toa head (toy version) turned upside down... so, technically, he didn't even have a real face, unless you count the one on the top of his head, looking backwards...
The second movie had Fire Drones — little machines built up using the CGI body of a Bohrok and the maskless head of a Matoran. And they did face the camera... but their faces were too tiny to see clearly. In the same movie, the animators even went as far as to show the comatose body of Turaga Dume with his mask on, even though it was a major plot-point that his mask had been stolen.
Freeze-framing the part when Kopaka turns Takua's mask back into position reveals through the mask's eye-holes that he doesn't even have a face, just a flat surface with his eyes stuck on it. Likely, none of the masked movie models had actual faces designed.
The titular Diabolical Mastermind of the French-Canadian animated series Belphegor is only ever seen with his gold mask on, which doesn't even have a mouth. One later episode has the characters tracking down an old film, as they discover a boy acting in it is the man himself. The audience is shown a cutscene of the film... with Belphegor's face obscured in shadow.
The General on Dastardly and Muttley in Their Flying Machines would always been heard only, via Dastardly's telephone, as just a lot of gibberish and throat-clearing. The General pays a visit to the Vulture Squadron on "Stop Which Pigeon?", and even though we still can't see him, we hear him and he sounds the same as when he's on the phone. Subverted in the Gold Key comics stories—he appears in Hanna-Barbera Fun-In #4 (drawn by Mike Arens) and #7 (Jack Manning).
Danger Mouse: In "The Statue Of Liberty Caper," we hear the mumbling of the U.S. President (translated by Secret Service agents) but we never see him.
In The Beatles episode "Thank You Girl," the boys' manager Brian Epstein is heard at the beginning (putting the boys on a diet and taking their money) but his face is never seen.
Motorcity: The character nicknamed "Red", always wears a mask (first his own, then the one provided to him by Kane), so his face has not been seen, which is also why Mike does not know why he holds a grudge against him.
In The Avengers: Earth's Mightiest Heroes, Baron Zemo never removes his mask during any of his appearances (and he's one of the show's most commonly recurring villains). Considering that we get a flashback that showed him getting infected by a biological weapon that he himself designed, which had the effect of apparently causing his face to meltnote though even in the flashback, we don't actually get a good look at him - at that point he wore a mask that looked more like a Klansman's hood, which was dissolved during aforementioned face-melting, to be eventually replaced by the skintight mask he wears during the main series, there's probably a very good reason that mask stays on.
Up until the first season finale, The Shredder was this. Most of his face was concealed by a large metal mask, leaving only his eyes (one that shows some a scar) exposed. During his fight with Splinter, though, his mask is knocked off and his entire face is revealed.