100 Deeds For Eddie McDowd: Has the titular character as The Faceless prior to becoming a dog (and since the show's been canceled, viewers will never know what Eddie McDowd looked like before he became a dog).
The Addams Family: Cousin Itt is effectively an example, as all we see of Itt's face is hair.
The Avengers: One episode features them looking for a missing elephant. The elephant is never shown and when Steed finds it, it's shown from the elephant's POV.
Also the Bureau 13 operative, only showing her mouth until The Reveal at the end of the episode.
Beetleborgs: Little Ghoul, a comic relief villain, was only ever shown from the front as eyes beneath a hood. Characters who saw her face tended to run off screaming.
The Big Bang Theory: Howard's mother is heard but never seen. She has been glimpsed twice so far: as a Freeze-Frame Bonus in "The Countdown Reflection" as the camera pulls back on Howard Wolowitz's wedding, and on "The Spoiler Alert Segmentation", where she is seen briefly walking by the kitchen door in the background.
Cheers: Norm's wife Vera. Usually The Ghost, she appeared in a couple of episodes as a sillouette, and in one episode is fully visable in the door of the bar ... just after being hit in the face with a custard pie.
The Dick Van Dyke Show: Alan Brady started out being talked about but never seen (meant to be ironic, since he was the star of the Show Within a Show while the actual show revolved around the unseen writers). However the writers (of the real show) found this too limiting after a while and started using Alan Brady in scenes, only with his face always pointing away from the camera. Eventually this was done away with too, and the audiences got to regularly see Alan Brady and scenes from The Alan Brady Show.
Maris Crane, who is also The Voiceless for a significant amount of episodes. The writers certainly enjoyed toying with The Reveal of both, but settled for The Unrevealfor the hell of it. Another problem, according to a season 4 DVD special, was that the writers had ascribed so many bizarre features and qualities to her that no human could properly play the role.
Martin's friend Duke is also a near-Faceless, although he appears briefly in two episodes.
Friends: Ugly Naked Guy, the only time we see anything of him.
Un Gars Une Fille (One Boy One Girl): A very common occurrence, as most recurring characters will never be seen, aside from their hands. This includes Guy's father, Sylvie's mother, Sylvie's best friend Loulou and her boyfriend Daniel, Guy and Sylvie's swinger neighbors, their therapist, Guy's business associate Geneviève, as well as many not-so-recurring characters.
Heroes: Sylar, until halfway through the first season; his face is shown for the first time in a flashback. This was mainly because the producers were still auditioning actors for the role until they hired Zachary Quinto.
Home Improvement: Wilson had the lower half of his face obscured by the fence in his yard; this later turned into a Running Gag where his face was half-obscured by other objects in scenes that didn't take place in the yard, and at least one instance where the top half of his face obscured but not the bottom half. In at least one press conference in real life, Wilson's actor, the late Earl Hindman, wore a miniature white picket fence over the lower half of his face. Another clip showing the curtain call at the end of the taping of one show also showed him holding a miniature white picket fence over his face. One Halloween episode had him dressed up as The Phantom of the Opera, with the mask covering the upper half of his face. Wilson made a couple appearances with face-paint on as opposed to a foreign object between him and the camera. Another episode had him completely on-camera in Renaissance Faire costume, wearing a fake beard. His face is finally revealed in the 'behind the scenes' episode. Al's mother also never shows her face, and it wasn't revealed in the 'behind the scenes' episode.
How I Met Your Mother: The Mother's face (as of the day before the season 8 finale) is never shown. It is usually obscured by her signature yellow umbrella.
The Lone Ranger: Once he dons his mask in the origin story, Lone Ranger is never again seen without it or some other form of disguise. (Given he rides around in the hot sun all day with the mask on, he'd need some sort of disguise due to the unusual tan lines.)
The Mary Tyler Moore Show: Phyllis Lindstrom's husband Lars. A clever variation came in a final-season episode where Johnny Carson is supposed to be the Special Guest at one of Mary's dinner parties. Just before he arrives there's a citywide power blackout, so when he shows up we only get to hear his voice.
The Mighty Boosh: Played for Laughs in the episode Tundra: Howard encounters a man whose face is completely shadowed by a fur-lined hooded jacket, who tells him to "look deep into the parka."
MI High: The Grand Master is always shown with his face in shadow or out of shot in a homage/parody of how Blofeld was depicted in the early James Bond films. Lampshaded in the episode where he is captured and Lenny comments that, despite the Grand Master being in a cell, he never managed to get a good look at his face (and he is taken to the prisoner exchange with a bag over his head).
The Millionaire: In this show, the mysterious benefactor, John Beresford Tipton, Jr.'s face was never seen. Usually just a hand, although sometimes other body parts, were seen.
Passions: Evil patriarch Alistair Crane. Initially only his hands were seen when his character appeared. When he was finally shown, the actor who played him died a short time later. He was replaced and was shown fully for the remainder of the series.
Al, one of the cops in the stationhouse was so tall that everything above his shoulders was always out of shot. Al often had strange things going on up there, including non-regulation headgear and strange haircuts; sometimes they were lowered into shot.
Subverted Trope in the episode "Rendevous at Big Gulch"; at one point, the camera remains fixated below the shoulders of the evil mob boss stroking his white fluffy cat as he goes over his plan to deal with the do-gooder protagonist. Right before cutting to commercial, he ducks into frame to deliver his final line.
Randall Flynn in his first appearance in "Chained Heat". Then, in "The Children's Crusade", he's actually seen. Turns out he's the same Department of Defense guy who offered to help Rachel and Ben with their project.
In "The Dark Tower", the President of the United States himself only appears as a silhouette and doesn't say anything.
Rhoda: "This is Carlton, your doorman." Played by Lorenzo Music, he was only a voice on the intercom.
Richard Diamond Private Detective: Sam. She was played by Mary Tyler Moore, but only seen from the legs down.
"The Continental" sketches have never shown the face of the woman who always visits (and ends up running from) The Continental, only showing the woman's hands (and, on one occasion, her legs and feet). It should be noted that the original version of the show from the 1950s did the same thing (use subjective camera angles to to make female audiences believe they were being romanced through their TV sets), making the sketch accurate for the most part.
The "Bill Brasky" series of sketches also used a faceless technique, where a group of drunken bar regulars converse amongst themselves discussing the ridiculously outrageous exploits of a man named Bill Brasky, who is never present throughout most of the sketch. Then, at the end of the sketch, you would see Bill Brasky finally appear, but he is only from the back of his head (never his face) and seen via forced prespective (as if a giant) and speaking in a deep baritone voice.
Seinfeld: George Steinbrenner. Also the boss of Tyler Chicken, who sounds exactly like George Steinbrenner. Both were voiced by Larry David.
Seven Days: The NSA board of directors in one episode were, rather oddly, covered in shadow.
If Oma's appearance in the cafe matches her real world face, then maybe Anubis' does too (or the face he had with his last host?), plus they find a sort of clone of him that is definitely not this trope (pretty boy good looks)
Used this trope a couple of times in the flashbacks featuring Ken Titus's many ex-wives and girlfriends (including the violent, manic-depressive schizophrenic Juanita, who was only The Faceless on a handful of episodes in which she wasn't prominently featured, but was mentioned by Christopher Titus whenever he talked about the differences between growing up with his Jerk Ass dad and growing up with his mentally-ill mom).
Also, Titus's first girlfriend (the brainy, yet abusive 5'1" Jewish girl who punched him in the face a lot) was The Faceless to the extreme when Titus first talked about her on "Dad Is Dead." The only thing viewers could see of her was her hands in a POV shot of her punching Titus with the caption "Psycho Bitch Cam" underneath. She wouldn't be featured in full until season two's "The Last Noelle."
Also from "The Last Noelle," Titus's second girlfriend, Taylor, was only seen from the back as she was cutting Titus's hair in his sleep and crying over her dead dog (the other two "psycho bitches" Titus dated — Dakota, who slept with a busboy at a bar, and Chastity, the Satan worshiper who had telekinetic powers — averted the trope, as their faces were actually shown).
Top Gear: The Stig, the "tame racing driver" of the British automobile Magazine Show. Always appears wearing a full face racing helmet with a dark visor which obscures his face. Also extended to The Stig's African cousin and American cousin in the African and American specials.
The Weird Al Show: In one episode, the Hooded Avenger gets so stressed he removes his mask... And is wearing another mask underneath.