In an attempt to reinforce the notion that the player of the game "is" the Player Character, most early games went out of their way to avoid applying any characterization to the player character.
More often than not, a thorough examination of the game will cause this to break down as providing any kind of substantial interaction with a player character who is a cipher is problematic. Most often, the first thing to slip through will be a tacit assumption that the character is male.
Less common in its extreme form today, as it makes anything like compelling storytelling highly problematic. Much easier to achieve in Interactive Fiction, for the same reason that text is better suited to the Tomato Surprise, and to this day, many text games still take this approach, and enthusiasts have been known to be disappointed if forced to play a character who does not reflect their gender or sexual orientation.
Beyond adventures, most games at least need to graphically present the player, so some amount of customization is required. The result is often an extended form of Purely Aesthetic Gender, with little additional influence on the story.
A weaker form of this attempt results in the Heroic Mime. Often used in conjunction with Second-Person Narration. Media which try to put a definite name and face on the protagonist result in Canon Name.
In most Real-Time Strategy games, the player is either a Featureless Protagonist or just a Non-Entity General who directs the action but doesn't even have a character.
This tends to cause problems when the work gets adapted to other media. One solution is to give the character in question as generic and bland a personality as possible. The other is to remove him completely.
Lone Wolf's title character is explicitly male from the outset, and his race, the Sommlending, are described as white-skinned and blond-haired. However, during the New Order Kai series, when the protagonist is one of Lone Wolf's top pupils, the narrative goes to ridiculous lengths to avoid calling him by name, mostly having characters refer to him as "Grand Master". There is even a random table set up in the books to help players generate their own Meaningful Name for their character.
Most Choose Your Own Adventure gamebooks portrayed "you" as a child or teenager of unspecified gender... who, in the illustrations, was sometimes slightly androgynous but almost always unmistakably Caucasian, and often clearly male.
There were a few books, however, where illustrations would consistently portray the protagonist as a tomboyish girl. Mystery of the Maya was one.
Jay Liebold's Mystery of the Ninja series started with a protagonist drawn as a boy with a ponytail, but the following titles made said main character a long-haired girl.
Fight for Freedom was set in apartheid-era South Africa, and with your dark skin a few bad things happen.
Edward Packard's Your Code Name is Jonah (reissued as Spy Trap) averts this, however, as your character is clearly an adult male. Which makes it more plausible since your character is a government agent.
Fighting Fantasy books never drew your player character and no-one ever remarked upon your gender (although the cover art for some of the early American editions would depict a generic fantasy warrior).
Another had you wake up in a sarcophagus with no memory; as such, you were some character of significance, and you had to learn about your past over the course of the story, culminating in a fight with the people that put you in the tomb.
The protagonist of GrailQuest is a young person named Pip whose body the player occupies. Pip was never referred to as any specific gender or illustrated from the neck up (with one exception, but then it was of Pip's head exploding so it was still gender-neutral).
The Destiny Quest books go to pains to avoid presuming anything about your character except for a few minor background details, even referring to you as "them" or "themselves" in dialogue when some kind of pronoun has to be used. At least in the first book, though, sometimes it slips and refers to you as male.
The protagonist in Banzai Run is never given any description aside from being a racer and male.
All that's known about the player protagonist in Varkon is that he's a Caucasian male with blonde hair.
In the solo D&D adventure "Blade of Vengeance", the pre-generated character is an elf whose gender is deliberately never specified, even on the enclosed family tree that names (and gives genders for) all the relatives he/she is attempting to avenge. The interior artwork depicts the PC as androgynous.
Video Games — Action Adventure
The main character in Overlord. Besides being male, all his features are obscured and blurred out by his impressive helmet. He's also never referred to by name by his former friend and colleagues. The later Overlords in other games are given some degree of Backstory, with the sequel starting him off as a Creepy Child along with several nicknames while the prequel Overlord: Dark Legend gives the Overlord the name Lord Gromgard though they still remain relatively faceless, wearing face-obscuring clothing before donning their armor.
Link from The Legend of Zelda series was originally meant to be this... in fact, that was the very reason he was named Link, because he was the "link to the gameworld", simply a player avatar. Ironically, he is now one of the most recognizable faces in all of gaming, endlessly tributed and/or parodied. Giving him a distinctive, recurring costume probably didn't help. This is most prevalent in the instruction manuals for A Link to the Past and Link's Awakening which are written using Second-Person Narration rather than referring to Link by name as Link. Nintendo is still trying to retain some of Link's Featureless Protagonist qualities (the reason he is still a Heroic Mime), he seems to be growing out of this in the later games, especially with regards to his personality. A notable shift is in Twilight Princess where the name Link is pre-entered on the Hello, Insert Name Here screen unlike earlier games where there is no default name and the field starts out blank.
Samus Aran from Metroid started as a complete cipher in both person and motivation (robot? guy in Powered Armor? who knew?). This caused some players to think "Metroid" was the character's name. Only at the end of the game did she get a gender and later aspecies, and her identity was only given any exploration in the later games.
Video Games — Action Game
The player character in Ghostbusters: The Video Game is one of these, as Dan Aykroyd and Harold Ramis figured that was the best way for the jokes to work. There is also an in-story reason: the team is still very shaken up by what happened to the previous new recruit so they refuse to learn even your name to avoid emotional attachments.
Interestingly, all the Ghostbusters wear easy-to-read nametags on their uniforms. Including the unnamed player character. Thing is, you have to work to see it, because you spend most of the game staring at your characters backside. If you manage to get a good look at it, you'll see it simply says "ROOKIE".
Assassin's Creed IV: Black Flag: All of the main Assassin's Creed games are actually simulations being experienced by someone from the present day, who needs to find something important in the memories. Due to the main protagonist's death by Heroic Sacrifice in the previous game the "main character" of Black Flag is about as nameless and featureless a protagonist can get. He or she is a Heroic Mime with no lines, and the present day segments of the game are also told in first person, and there are no mirrors so the player can't even see their character's reflection.
Dark Fall: The Journal is bold enough to give the player character a nationality and approximate age range, but still sees fit to leave the character genderless. The full name of the PC's brother is given, but there's no guarantee that the PC is male or single, so may not share the same surname as him.
In The Journeyman Project, the player is only referred to as "Agent 5", and though we see his reflection, his face is computer-generated and featureless (all other characters are photorealistic). He gets a full name (Gage Blackwood), identity, and face in both of its sequels, as well as the remake, Pegasus Prime. Perhaps as a bit of Lampshade Hanging, in the second game, the player comes across an action figure of himself (the events of the first game had been turned into a popular action movie) with the same mannequin features.
The player character's gender in the Myst series is never made specific; Atrus only ever refers to you as "my friend." Thanks to the Myst games being a series however, the need for a persistent player character is met quite cleverly, by only providing "hints" here and there about the character as they become Atrus' family's friend. This more encourages players either to perceive themselves as part of the story or use their own imaginations, rather than leaving one to wonder who they're playing. The avoidance of even hinting at gender might almost be called impressive — though a couple of points in the series do present players with the ability to create a customizable character.
It should be noted that Word of God places the first four Myst games some two-hundred years in the past, which breaks the concept of "the player as him/herself" somewhat. Both Uru and Myst V are set in the present (with certain key characters still alive because the D'ni live very long) and therefore feature a different protagonist. In Uru it's explicitly meant to be the player (one of the meanings of "Uru" is "You Are You"), but recent Word of God has declared that the protagonist of Myst V is Dr. Watson of the D'ni Restoration Council (an NPC in Uru, and the in-universe counterpart of developer Richard A Watson).
Though a non-canon storyline/walkthrough for the original in the Prima Strategy guide alludes the player character as a male photographer from modern day finding the Myst book in a dusty old library which apparently sent him backwards in time. Other than that, the character in the guide is curious, clever, reacts to the few jump scares the game has with obvious results, and is slightly snarky, especially when Sirrus and Achenar start to threaten him if he doesn't bring more pages. "Player: You're a book, what are you going to do? Throw footnotes at me?"
The only personal information established about your in-game persona in Riddle of the Sphinx and its sequel The Omega Stone is gender, which you can choose in the second game. The only time it ever comes up is in found letters' being addressed either to "sir" or "madam".
In Shivers and its sequel, though the player is given a home town and set of friends, he is only ever referred to by others as "You", and only ever described in gender-neutral terms.
Except near the very end when you fall down a large slide and your screams are clearly masculine.
The Crystal Key, like Myst, handles this by showing everything from a first-person perspective and having almost no one with whom to interact (the occasional enemy soldiers don't speak your language). Unlike Myst, however, items don't teleport from the main screen to your inventory and back again—they levitate, as if you're telekinetic. Also of note is that you abruptly stop being a Heroic Mime if you're caught and tortured, but gender neutrality is still preserved—the resultant screaming is barely recognizable as human, let alone male or female.
Some games give your character a gender-neutral name (e.g. in Rhiannon, you're "Chris") to allow some sense of identity without excluding any gender.
DoorBot:"Human being isn't it? Well, ones heard mixed reports..."
Video Games — Edutainment Game
The hero of the Super Solvers series wears a giant hat, a giant coat with the collar turned up, bermuda shorts and tennis shoes. Either the hero's skin is stark white, or they're wearing tights...
The player character in almost all Carmen Sandiego games is completely faceless and unidentifiable, only referred to by their rank (Senior Investigator, Gumshoe, Master Detective, etc.) The NPCs you typically speak with to gather clues never reference the player, outside of "How do you do?"
Video Games — First Person Shooter
Word of God says this is the reason why the DoomMarine never talks. He was meant to be the player character, and thus was never given an official name and never speaks. Played less straight than other examples as you do know what he looks like, but nevertheless, he was meant to be the player.
BioShock starts out like this — the only clue to your nature are your hands, which are white, kind of masculine and have little tattoos of chain links on the wrists; and your voice, heard only in the opening cutscene, which has a nondescript American accent. Then it gets weird and you find out the details of your identity. Jack also seems to lack a shadow, but that's an oversight on the developer's part.
If you examine the photographs pinned up right outside Ryan's office, you can see Jack's face captured in a couple of them.
If you pay attention, you'll notice that Jack is freaking huge, assuming that everything in the game is made for normal human size, he is easily seven feet tall. It does explain how he can convincingly disguise as a Big Daddy.
In the sequel, the protagonist has a name (Subject Delta) and an appearance (Alpha Big Daddy), but lacks any speech or real personality.
In BioShock Infinite the player character Booker Dewitt possesses a name, voice, appearance, personality, fleshed-out backstory, and a clear driving goal.
The protagonists from System Shock games. The first games features a normal looking male white hacker with the mullet, and the second game has the male white soldier with cyber-eyes. Other than that, everything else is for the player to imagine.
In the original Halo trilogy, the Master Chief John-117 never shows his face, speaks only a handful of lines during cutscenes, and is referred to almost solely by his rank. The one time he takes off his helmet, the camera angle shifts to obscure his face just as he removes it; even when using cheats to keep his head in frame, all we get to see is another helmet! He has a bit more personality than usual examples of this trope, though.
His character is heavily expanded on in both the novels and the comic book adaptation of The Fall Of Reach, which also reveal that he is a Caucasian with brown hair, though the only clear visual depiction of his face is of him as a six year old.
The series drifts away from this in Halo 4, since the developers were specifically aiming to explore the Chief's personality. He speaks during gameplay as well as cutscenes, and the Legendary ending even gives us a brief glimpse of the area around his eyes when he takes off his helmet.
The Rookie in Halo ODST never removes his helmet or says anything. The only clue about his appearance is his fingers, which are white. His initials are apparently "J.D.", but that seems to be more of a reference to the generic placeholder name "John Doe". He gets a little more characterization in the Halo: Evolutions short story "Dirt", but not much.
SPARTAN-B312 AKA Noble Six, the protagonist of Halo: Reach, is perhaps the ultimate example of this trope in the series, since the player gets to determine everything about the character from the gender to the appearance of the armor. S/he only speaks a handful lines, and we never get to see even a micrometer of him/her that is not covered in armor.
In Marathon, the protagonist is drawn in a few art pieces, but his appearance is very inconsistent. You can only see what he looks like in-game in co-op, and he's wearing what looks like a flight helmet, which only reveals his jaw.
Notably, the game files of Half-Life 2 don't contain a character model or skin for Freeman at all: since there are no reflective surfaces or (legitimately accessible) third person perspective, the player never gets to actually see anything but his arms. The only reference to Freeman's facial appearance is on the game's box art.
In the early (or just pirated) version of the game it was possible to look at your PC head, which revealed a mannequin face not actually covered in textures.
The more recent Call of Duty games have this in effect for most of the multiple player characters, who never speak and are never seen in third person. One notable exception is 'Soap' MacTavish, who is the primary player character in Modern Warfare, but your squad's commander in the sequel, in which he has a full speaking part.
Averted with Alex Mason and Jason Hudson from Black Ops, who are both fully voiced. Hudson appears in some missions where you play as Mason, and Mason's face is shown a lot in the between-mission cutscenes.
The only thing we know about Alcatraz, the Delta Force Marine in Crysis 2, is that he's fond of tequila, unlike the prior protagonists of the series who both had voices, personalities, and faces. The tie-in novel Crysis: Legion does expand on his character a bit.
FEAR's lead protagonist, Point Man, is, aside from being specified to be male, basically a Featureless Protagonist. This is actually practically canon, considering that he is later revealed to have no memory and be one of a number of clone soldiers birthed by Alma. The third game finally revealed his appearance.
The Pyro from Team Fortress 2, whose nationality (notable considering s/he's on a team of national stereotypes) and gender are unknown. Never removes that gas mask, is known only by Pyro, and speaks only in muffled grunts. S/he does have some characterization though.
The release of the long awaited Meet The Pyro video finally clears up some things. Namely, that the Pyro is completely insane. While the other characters talk of the monstrous engine of destruction that is the Pyro, who even scares the people on his own team, we get to see things from the Pyros point of view. Apparently, he thinks he's doling out rainbows and love rather than fire and death. Nothing else is learned about the Pyro, as even in his/her own mind, (s)he's still wearing the gasmask.
Compounded by the fact that Pyro is alternately referred to as "he" and "she," sometimes within the same sentence. "He's not here, is she?"
That can be chalked up to simply Valve trolling everyone. The Scout clearly says "He's not here is he?" in the video, but the transcript uses both pronouns. This video from The Game Theorists analyzes the Pyro's character model and other hints, and determined it's likely a homosexual man. But hey, it's just a theory. A Game Theory!
In Receiver, the protagonist does not even have a character model. Your weapon simply floats in the air in front of you.
Video Games — Interactive Fiction
The Interactive Fiction game Everyone Loves A Parade appears to use this. However, it subverts it. Towards the end of the game, you learn that your character is decidedly female. Using this to your advantage is necessary to actually complete the game.
Interactive fiction game Jigsaw takes this to extremes: Neither the player nor the main villain is ever referred to by gender-specific terms, but only by the names "White" and "Black" (after their costumes), but are taken to be whichever pair of genders the player is most comfortable with, given their evolving romantic relationship. That said, a number of details from the game have been taken to suggest that the two are almost certainly of opposite genders (you are taken to be a honeymooning couple at a time in history when homosexuality is illegal). It is also possible to provoke responses indicating that both Black and White are male, though this is believed to be a bug. One scene set aboard the train bringing Lenin to Petrograd just before the Russian Revolution requires the player to don the uniform of a British Army officer. However, as many people have pointed out (including the game's author), stories of women passing themselves off as male soldiers in times of war are not uncommon in fiction, nor are they unheard of in reality.
Jigsaw's predecessor Curses was very similar in its presentation, but without the romantic aspect involved, the question was not as urgent.
Downplayed in an interesting way in the Interactive Fiction game Leather Goddesses Of Phobos. The game plot features several instances of (heterosexual) sex, so in order for the genders to "match up" the player had to specify his or her gender (but no other details about their character). This was done by making the player go into a restroom — either the men's or women's room.
Since you control a First-Person Ghost and are responsible for all your own dialogue, Facade can involve nothing but this. Trip and Grace will automatically assign you a gender based on the name you pick from the list, but then, you can spend the get-together asserting that you're honestly and truly a woman named Gonzalo and it could be perfectly in-character for that session.
Averted in several Infocom games, especially those based on licensed properties such as The Hitchhiker's Guide to the Galaxy where you are Arthur Dent. Or James Clavell's Shogun where you are John Blackthorne and in Sherlock: Riddle of the Crown Jewles, you are Dr. Watson. In Plundered Hearts, you are clearly a female. In Arthur, you are the youngster who will be the legendary King Arthur.
Arguably somewhat made diffucult in certain games due to the backstory. In The Witness, you are a 1930s "gumshoe" private detective and a hostile female calls you "shamus" (a slang term for private investigator) at one point. Given the dated setting of this story, it would be unusual for your character to be anything but White and male. Hollywood Hijinx makes it difficult to put yourself in the position of the player character given that the background story gives you a rich eccentric uncle and aunt that you may or may not have in real life. Infidel has pictures of the player character on the box and in the games feelies which clearly depict a White male. Last but not least, in A Mind Forever Voyaging, you are not even human, You are a computer!
Video Games — Mecha Game
In the original Mech Assault, the main character was a Featureless Protagonist. As new gameplay elements of the sequel required an onscreen avatar for the main, they were revised into an explicitly male Heroic Mime — to the disappointment of anyone who had previously imagined him as female.
The MechWarrior series has done this for the second game and it's expansions and the third one as well, which they commonly referred to you as "commander" or "lance leader". It stopped around the expansion to the third game when the player character was given a voice, name and gender for each subsequent game since.
Chrome Hounds uses this; it's fairly easy since it's a mech game.
Armored Core does this as well, referring to the player only as "Raven" or "LYNX".
Perhaps as a nod to this, though slightly characterized, the player character in The 7th Guest is referred to in the manual as "Ego", Latin for "I", and starts the game with absolutely no idea how he got there or who he is.
The player character in the Dark Parables games is only ever identified as "Detective," and never seen. At most you see gloved hands and jacket-covered arms.
Similarly, the player character in the Ravenhearst arc of Mystery Case Files is also only called "Detective" or "Master Detective." There's a slight subversion in these games, however; at the end of Madame Fate, the character's voice is heard speaking on the telephone, revealing that the Master Detective is in fact a woman.
In the Collector's Edition of Fate's Carnival, you can collect bobbleheads of many characters throughout the series. The Master Detective bobblehead is masked and wears a full-length overcoat, making for a very generic figure.
A Dark Room has this for the protagonist and most other characters, although some are assigned genders.
All one ever sees of the detective in the Mystery Trackers series is gloved hands.
Video Games — Racing
Destruction Derby games always have these. You're represented by a person whose face is fully obscured by a helmet.
Depending on how much story there is, this can be common. Even when you're in the roofless 1880s-era Mercedes early car in Gran Turismo, you're still in your firesuit and helmet. And taken to an extreme in the Burnout games, where no-one at all is driving.
Same for the Need for Speed games. The PC's face is either obscured by a helmet, or pixelated.
Notable in the first to third games that the windows of the cars are black and opaque enough to be considered illegal.
The player character and his B-Spec drivers in Gran Turismo 5.
Video Games — Real Time Strategy
As mentioned in the description, most RTS games simply have no player character beyond a Non-Entity General.
In the Command & Conquer games, the player is only ever addressed as Commander/Comrade General (or other appropriate rank). In fact, the original Command & Conquer played as if the game was an actual command interface and the characters adressed the player directly, though subtext with your female assistants in later games assumes Most Gamers Are Male. There are some aversions though:
Tiberian Sun averts this trope as the player actually has a specific character who's seen in cutscenes: Anton Slavik for Nod, and Michael "Mac" Mc Neil for GDI.
In the initial mission of Kane's Wrath, it's implied that the Nod Commander in Tiberium Wars proper is supposed to be one of the grunts down on the field, while at the end it's revealed that you are LEGION, successor to the mad AI that is CABAL.
Your character in Tiberium Twilight appears to be male, inferred from dialogue with the (still nameless) Commander's wife Lily, and your undergoing plastic surgery to resemble Kane during the story.
The Commander in Dawn of War 2. No information is given about him except that he is recently promoted, a man of few words (he doesn't have any lines - not even unit responses) and so awesome that he is expected to beat back an ork invasion on his own.
In StarCraft and its expansion, the player character was called by titles such as Magistrate, Cerebrate, or Executor depending on what campaign you were playing. Later synopses of the game universe's history state that Artanis was the Protoss Executor, seemingly ignoring the fact that he was a separate character in Brood War and wasn't even an Executor (he was a Praetor, although this was Retconned).
Video Games — Role Playing Game
The original release of Dragon Quest IV allowed the player to select a name and gender for their ultimate main character (though unusually, you wouldn't actually get the character until very late into the game, and so could easily be confused when the game first has you playing someone else). However, this breaks down at many points, especially in bath scenes that have decidedly (and presumably unintentional) Les Yay overtones if you're playing a female character.
The DS version of Dragon Quest IV lets you choose your name and gender again, with some of these incidents corrected. They also added a 'Prologue' that lets you see your hero briefly before the main game begins.
Dragon Quest III also allowed you to pick the name and gender of not just your hero, but the rest of your allies. Again, in the original translation of the NES game, several referred to you as 'Ortega's son' — starting with the king himself. This was corrected in later versions, though. Corrected with a Lampshade Hanging: "Ortega's Son... er, I mean, Daughter!"
Dragon Quest IX lets you customize pretty much everything about your hero's (and his/her companions') appearance... and then forces you to don a suit of "Dragon Warrior Armor" whose mask covers your face for a climactic battle and cutscene late in the game!
In The Elder Scrolls series of games, you can customize your protagonist, but when a character or an in-game book refers to the protagonist of a previous Elder Scrolls game, the said protagonist is always a Featureless Protagonist referred to with a nebulous nickname ("The Eternal Champion", "The Emperor's Agent", "The Nerevarine", etc.). The game does not know what kind of character you played the previous one with.
This leads to some goofy scenarios where features about the protagonist are assumed. In Skyrim, when a character reacts to your appearance they generally react as if you're a scrawny unimposing kid and on the stupid side even if you made your character look like a muscular grizzled badass and have him equipped in dragon scale armornote which you can only get by killing a dragon and crafting the armor yourself because the dragons only just recently returned to Skyrim.
The first and thirdFinal Fantasy games apply all characterization to your whole party; the individual members are completely interchangeable. This is especially true in III, where you can change your characters' very identities at any time through the job system — all they have to call their own are their names (which you chose).
This is nodded to in Dissidia Final Fantasy: Onion Knight and Warrior Of Light are called by their class and title, respectively — the Warrior says he doesn't remember his name (because he never had one; it was the player's choice).
The DS re-release of III gives all four characters their own names, personalities and backgrounds, and they each have their own character models for every single possible class.
Etrian Odyssey does this in two ways. One being that all of your guild members have absolutely no background, name, gender, or anything. It's up to you to give them a class, a face (which also defines their gender), and a name.
The other occurrence would be the guild leader. Being impersonated by the player, he even only gets vaguely mentioned in the beginning as one of many daring explorers who are willing to challenge the labyrinth. And the games seem to assume that it's a "he".
Strangely, the guild officer in Etrian Odyssey 2 invites you to register yourself as a member (i.e. name a character after yourself), but the system isn't designed to recognize which character is "you." If you take her up on her suggestion, the narrator will refer to you and your avatar as separate people for the rest of the game.
In the Game Boy version of the Pokémon Trading Card Game, the player character portrait is shown as a bust portrait with young, tween-like facial features of ambiguous gender, an ethnically unclear anime look, and hair tied up in a bandanna on the forehead though it's clearly black.
Pokémon X and Y is a much straighter example. Not only can you choose your gender, name and now your skin color at character creation, but every other part of your trainer is customizable even after that point. Hair color? Sure. Haircut? Why not. Clothing? A dizzying array of options await you, especially once you have access to every city. The clothing options vary so much that it even gets hard to assign an exact age to the protagonists.
While you do get to customize the player character in White Knight Chronicles to a ridiculous degree, in cutscenes (s)he doesn't actually do anything other than stand around and watch the other guys talk about stuff.
Fallout 2 does this somewhat to the player character from the first game. There's a journal entry in the manual from the first game's PC talking about what s/he did after getting exiled from Vault 13 which never states his/her name or gender, but does state that s/he does eventually settle down and get married...to a spouse of indeterminate gender with an androgynous name. Eventually, the player runs across a statue honoring the character from the first game, but the text on the statue calls the character "he or she."
As in Armored Core, King's Field, and Shadow Tower. FROM Software's third-person view Demon's Souls and Dark Souls also use this, but add the option of appearance customization. In the former the character is a person who wanders into Boletaria's fog (for reasons assumed to be exploration, heroism, pillaging, etc) and is referred to by the Maiden in Black as the "Slayer of Demons." In the latter, the character is an Undead who awakens and escapes from the Northern Undead Asylum and is referred to as "The Chosen Undead" by Frampt/Kaathe (of course whether or not this label is accurate depends on how you read the story). The protagonist does not speak other than Yes/No and actions, this actually plays into the games online component where your only method of speech is gestures.
In 7th Dragon each class has four portraits, two for each gender. One portrait in each class would be a Rushe, a race of elvish or cat-people depending on the gender. There are no default names for each portrait except for special names that would give one extra skill point to the class. In 2020, there are only two portraits for each class and the Rushe are gone.
Always Sometimes Monsters attempts to avert this as part of its Central Theme about the importance of choices. While the characters you can choose from all have pretermined appearances and genders, you can still choose whether to play as a male or female, their race, and their sexual orientation. This impacts how others treat you, and can open or close doors accordingly. Somebody might deny you a job opportunity based solely on your looks, for instance.
Video Games — Simulation Game
The Freespace series of games, where the player is only ever addressed as "pilot" or by the wing position "Alpha 1". Just like all the other Red Shirt wingmen, except the Red Shirts actually talk, so they aren't exactly Featureless Protagonists. The only thing we know is that the PC is Terran ("Terran" being the only name the Vasudans use to address the PC, ever).
Subverted in Ace Combat 3: Electrosphere. The Player Character turns out to be an AI. The planes you were flying the whole time? They were completely unmanned.
Ace Combat 5 comes really close to revealing the player character's face. The one thing that stood in its way? Chopper's elbow.
Star Trek: Bridge Commander plays this straight. You are the nameless Captain (or maybe your name is Captain) of a starship, and nowhere, anywhere, can you get a glimpse of yourself. The entire game runs in first person view. However, a Ferengi is outraged that you allow a woman (your First Officer) talk to him. That makes you very likely male.
In Red Baron the player character has no real characterization whatsoever beyond the player-input name. It can be reasonably deduced that he's male, but this is due to the fact that, other than nurses, there were no female personnel in any of the major armed forces during World War One (officially).
Aerobiz: The player is only known as the CEO and always addressed in second person ("You").
X3: Terran Conflict and X3: Albion Prelude only ever address the player as "pilot" or "captain". You can rename your PC, but it never has any effect on gameplay.
Video Games — Stealth-Based Game
The original Castle Wolfenstein games cast the player as an unnamed Allied POW captured by the Nazis during WWII. He would not be named until Id's 3D FPS remake, Wolfenstein 3D.
In Crackdown, you are only ever called "Agent". The only certain thing is your gender, as there are no female Agent models.
Video Games — Tower Defense
In Plants vs. Zombies, the protagonist doesn't have much discernible characteristics. But since they have a tricycle, it's an almost-certainty that they are a parent, and probably a single parent. Crazy Dave considers the protagonist a neighbor, so it's also likely that the protagonist own the (rather nice) house, which means that they are likely to be middle-class.
In the trailer for Plants VS Zombies 2 it shows Crazy Daves house, and one framed newspaper clipping says "Crazy man saves world" so one could guess that the player from the original is Dave all along and he's been talking to himself the whole game. Why? He's crazy.
Video Games — Turn Based Strategy
Advance Wars puts you in the role of an "adviser" to the Orange Star Army, who is spoken to directly but never shown onscreen. Absolutely nothing is known about your character except that they are new to the job. In practice, your "advising" consists of telling the various generals what to do (they never go against your advice) and they in turn deliver these orders to their troops. This makes your character seem a bit redundant, which is probably why the adviser was removed completely in Advance Wars 2, which puts you in control of the generals directly (which is basically what you were doing in the first game).
Fire Emblem: The Sword of Flame does this, too. You're a wandering tactician, and you meet one of the main characters before the first fight. Of course, after the prologue chapters, you're rarely mentioned.
You can actually choose to not have a tactician, in which case the sprite will not appear on the map and the characters will not address you. However, this also means that Athos won't give you the Afa's Drops (a very good item that is almost a must to use on characters like Nino), because he normally hands them to the tactician personally! Otherwise, the differences are fairly minor.
The exceptions are Fire Emblem: New Mystery of the Emblem and Fire Emblem Awakening. My Unit/The Avatar can either be a boy or a girl, and their looks are freely customized by the player. In New Mystery, you can also choose their fighting class; and in Awakening they have their own Class, the Tactician (which is similar to Magic Knight)... and even have love interests, marry them and be the dad/mom of their kids. Including the main Lord Chrom, if the Avatar is a girl.
And yet in the love confessions and the plot-important CG's describing their in-story position as the Soul Jar of Grima, the Avatar's face is never clearly shown.
Faceless (and even more so, nameless) protagonists are becoming a Dead Horse Trope in visual novels now days. More story-based games sometimes maintain the faceless look early in the game, but then reveal the protagonist's face in cutscenes later in the story when the player has gotten to know the character better.
In most dating sims, the male protagonist (being, effectively, the player's stand-in) when he is on screen is a vaguely dark-haired youth whose bangs conveniently hides his face if he is ever seen from the front. Dating sims with female protagonists, and sound novel-type dating sims, tend to avoid this and do show the girl's face from the beginning.
Toyed with in the Prince of Tennis dating sims. The first one, Gakuensai no Oujisama, never shows the face of the brunette main girl note (default name: Shizuka Hirose), and there are extremely few mentions to her possible looks (i.e., Kawamura's path implies that she uses glasses). In the other two, Umibe no Secret and Sanroku no Mystic, the girls's faces are clearly seen from the beginning (Sanroku's Tsugumi Obinata is a long-haired girly girl, Umibe's Ayaka Tsujimoto is a short-haired tomboy), and yet sometimes the CG's deliberately show them only from behind or from angles where we cannot see their faces, despite us already knowing how they look like.
The Shall We Date? games, however, play this trope painfully straight. They take great pains to never show the otome protagonist's face even during the kissing scenes!
The Tokimeki Memorial Girl's Side games give the heroine a defined appearance, that of a generically cute girl with reddish-brown hair in a bob cut, but she's only fully displayed as a Super-Deformed sprite in game menus and minigames, while CGs typically avoid showing much more than the back of her head.
Higurashi: When They Cry only pretends to be a dating sim at first, so it follow this trope for half of it. Later it is revealed the protagonist is someone else and the previous main character gains a face (the new protagonist was present since the beginning, so they had a face already).
Its sister series, Umineko: When They Cry, however, averts it, by giving the main character a face from the beginning. The author even commented he wanted to avoid having the main character go faceless for so long again.
Higurashi also played it straight with a third protagonist of sorts. As the sequences taking place outside of the Fragments in which you were only described as a "Special Existence". Sometimes it seemed to be Breaking the Fourth Wall and other times suggesting that you were a genuine entity within the game's universe. This trope most comes into play in the first such encounter, in which another spirit being refers to you as it's sister. However they then point out that you might be a boy, but telling the gender of such beings is complicated. These sequences were also in second person, in contrast to the rest of the novel.
Averted all the time in Key Visual Arts' works, since the male protagonists actually develops a character (especially in CLANNAD. It would be ridiculous if Ushio-chan have a faceless dad.). Some protagonists are more bland than others, though (i.e. in Planetarian).
Little Busters! takes it even further - Riki does have sprites, though they only show up in special situations, and while most CGs don't show his face, a fair few still do. He even has a voice, though he only speaks during batting practice, while battling, during the scenes where Masato, Kengo, or Kyousuke become the POV character, and in the scene where the boys disappear.
Averted in Katawa Shoujo, as we see Hisao Nakai's face clearly in one of the first CG's and his features are almost never hidden from then on. He also has an established personality, though some of it does vary from route to route, which could be either attributed to the influence of whom he spends time with on his personality, or, if you're feeling less charitable, just chalked up to a case of Depending on the Writer. Oh, and he has arrythmia, meaning that not only do he have a name, face, and personality, but also a medical history.
In One Kagayaku Kisetsu E this is played up to the point of stupidity. In CG in which Kouhei is kissing someone, he will have no eyes, nose, etc. depending on the scene.
The protagonists of the Romance Games produced by Voltage Inc are depicted without eyes when they appear in CGs - sometimes by the use of a Blinding Bangs effect, but often their faces are simply blank where their eyes should be. The short introductory animation of Office Secrets does show the protagonist with eyes, but in the in-game CG that the footage was based on, she's eyeless.
In one of the spin-offs of In Your Arms Tonight, it gives you the option of displaying the MC's sprite, which gives you a clear image of what she looks like, face and all, subverting this trope.
Success mode in MLB Power Pros averts this with your avatar being customizable and shown all the times throughout the game; while the character itself is portrayed as a local Idiot Hero who loves baseball. It helps that half of the gags come from your avatar's hilarious facial reactions.