Squall Leonhart of Final Fantasy VIII has a facepalm as one of his stock gestures, and he uses it often. The mannerism is iconic enough that it was carried over into the Kingdom Hearts games as well.
The opera Impresario, who's very sensitive about his operas, does this when an act goes wrong or when it may go wrong. It is probable, though, that his "face palm" is more of a corny, theatrical and/or dramatical gesture of distress, (you know, that old cover-your-face-with-your-arm/hand-whilds-wistfully-going-"Oh" thingy,) rather than the common, slightly more humorous usage of the gesture. This would make sense seeing as he is, well, the impresario of an opera.
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A straight example of this occurs when Gau leads Sabin and Cyan to a cave, to show them a "shiny shiny". Once they arrive... he forgets where it is, cuing a facepalm.
Lulu responds to a lot of Tidus's and Wakka's shenanigans by burying her face in her hand.
When Yuna emerges from an Al Bhed ship, having beaten up its crew - rendering your party's rescue pointless - Lulu, Kimahri and even Tidus are shown doing this at once. Then the normal victory music plays.
Wakka does it when the party arrives in Luca and Tidus grabs a megaphone and starts shouting trash at the Luca Goers.
Fire Emblem: Kent, whenever Sain starts making his moves on a girl. See on the right hand side here◊.
In Dead Space, the main character does a facepalm after he learns that his girlfriend, who he thought was alive, was Dead All Along. A sad facepalm indeed.
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In the Professor Layton series, both Layton and Luke do this if they get a puzzle wrong. Layton pulls the brim of his tophat over his eyes, while Luke does the classic forehead slap.
In Utawarerumono This is Eruruw's default expression for when Hakuoro does something stupid — but not stupid enough to get seriously angry over (which he does often).
World of Warcraft added a /facepalm emote in patch 3.0.2, although it only produces a predefined text message and not animated. It's also one of the few emotes the game's statistics page will track on your character; they expect you to use it that much.
Anarchy Online as well added a similar command, and animated it.
Guild Wars also has a facepalm emote, though the command for it is /doh.
In 2011, players who liked the City of Heroes Facebook page on July 21 or between August 17-31 received the /facepalm emote ingame.
Tales of Monkey Island gives the second-most-intelligent character in its opening sequence (namely: a monkey) one of these right before everything goes to hell.
It was only logical that the facepalm became an emote in Star Trek Online.
The Spy class on a losing team can be seen face palming if he is still alive during the aptly named "Humiliation" phase. He also does this in one of the official comics: In "A Smissmas Story", he face palms and rests his head on the desk when Soldier (acting as Spy and Scout's lawyer) encourages Scout to go with a completely ludicrous testimony.
The Sniper does the hat version in his "Meet the Sniper" video when he's trying to talk to his father on the phone.
In BlazBlue Jin and Hakumen facepalm if they lose to Time Up.
In another Arc System Works example, this is Baiken's taunt in Guilty Gear.
Dark Forces Saga: Kyle Katarn will do this when he gets bored game-over due to some reason other than his own death.
Shepard: You have a ship named Qwib Qwib? Tali:(facepalm) Oh, here we go...
Mass Effect 3: Shepard has this reaction to seeing Conrad Verner yet again.
In the Citadel DLC, this is Miranda's response to Shepard suggesting that she sleep with Jack, Liara's response to James's attempt to claim that physical conditioning trumps biotics, and EDI's response to Joker replying to Shepard's offer to dance with her when Joker won't by laughing his ass off for 30 seconds straight.
In Sonic Colors (Wii version), Sonic does a facepalm in the cutscene where Tails is attempting to figure out what the Wisps are saying. ("He says his name is Talks-a-lot and he's from a far off soda...") Yacker (the Wisp Tails was trying to translate for) also facepalms. At the exact same time as Sonic does.
Sonic facepalms up to twice more throughout Sonic Generations. First time is if Chemical Plant Act 2 is the second act of that level to be completed—after Amy speaks her line, Modern Sonic facepalms. He facepalms once more during the Reveal.
If you're watching him, Raz pulls this off during the boss fight in Black Velvetopia. It's not the main focus, but not easy to miss, either — just pay attention to him while Edgar reverts to El Odio.
While we're on the topic, Sasha gets the chance at the end of the game, when Ford's psitanium wears off and Chef Cruller returns.
Also done in Brütal Legend (which is from the creators of Psychonauts). During the intro, the band Eddie was a roadie for starts their new song with a really badass and edgy guitar riff...only to transition into sissy pop singing. Eddie then facepalms.
If you play the game In the 1st Degree right, Tobin will do this shortly after having a meltdown in the courtroom. This is probably due to him realizing that he just effectively hanged himself.
In .hack//G.U., Haseo does this so often it's one of his standard animations.
Jansen the drunken miner: My farm supplied eggplant to half of South Reach! Other drunken miner: Oh yeah? Well, my eggplant supplied half the bastards in South Reach! (drunken laughter) Hawke:(facepalm)
Sarcastic Hawke pulls another one during the quest where he/she looks for an escaped prisoner in Act 1.
Lia the kidnappee: He didn't mean to hurt me! There are demons who made him do all these horrible things! Hawke:(facepalm) I should remember this one. "A demon made me do it."
Ken does this in Super Puzzle Fighter II Turbo when his playfield his halfway full of gems.
Seen in the PlayStation 3Updated Re-release of Eternal Sonata in the Lament Mirror dungeon. Frederic Chopin is stuck alone with the eight-year-old Salsa, who is whining about a lack of food, and asks him to use his magic powers to create a steak. He tells her that magic is not a tool of convenience and she throws a full-on tantrum, causing him to facepalm.
In Star Wars: The Old Republic, on one of the Sith Warrior missions you have the option of sleeping with Lord Grathan's wife. Later you can brag about it to Darth Baras, prompting a facepalm from Vette.
Poker Night 2: Ash will do a dramatic double facepalm if he's not pleased with the hand he's dealt. He'll then proceed to try to bluff his hand after that.
It's easy to miss in Carrie's Order Up!, but should you lose a life while Calcia is on screen, she'll faceclaw at Carrie's clumsiness.
In Star Ocean: The Last Hope, Edge can't help but do this after a strange conversation between Sarah and the King of Astral in which she gives him the "gist" of an official letter that she's apparently had for more than three years and had forgotten to give him up until then. (She says she was fifteen when she got the letter. The game's dictionary gives her age as 19.)
In The Legend of Zelda: Breath of the Wild, Link does this when Vilia's drag disguise is partly uncovered by a gust of wind and the latter tries to brush it off. Paya also tends to cover her face with both of her hands when getting flustered while talking to Link.
Whereas Marie slumps over with a dreadful look on her face when she gets mouthy, Marina of Splatoon 2 offers a cute smile after doing this over some of Pearl's derpier moments, like confusing "stakes" with "steaks".
Clarence's Big Chance: Clarence's girlfriend will do this if he performs badly enough.
Roland gives one after Evan keeps betting against a guard in a dice game who is using a dice that seems fairly obviously rigged and ends up ten million guilders in debt.
Later, it's Batu's turn when Evan agrees to help out a Grimalkin (cat-guy) named Tabbias in one of the game's many sidequests.
In Dragon Quest XI, Jade does one if she messes up on the Electro Light pep power, summoning mechanical monsters instead of the hoped for Metal Slime monsters.
Yoshi's Cookie: Chef Mario does this when the player gets a game over.
In Cooking Stars Freddy buys a pie oven and Nancy asks if he actually knows how to make a pie.
Freddy: I can chop fruit very nicely. Nancy: Leaving it up to me to do everything else. [facepalm]
In NEO: The World Ends with You, Minamimoto facepalms in restaurants if you're about to feed him something he doesn't like or he's already full.
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