In Boku Wa Tomodachi Ga Sukunai, Kodaka does one in episode 3 at the pool, after he defuses a confrontation between 3 guys and Sena. She then stops them from leaving, only to continue insulting them, and forcing Kodaka to save her yet again by utilizing his Face of a Thug to scare the three guys away. He later berates her for acting that way.
Rin in Fate/stay night does this a lot. She even has a number of different kinds of facepalms.
Several characters in Mahou Sensei Negima! do this, especially Chisame and Asuna, whenever she has to put up with Ayaka.
Kyon◊ does this relatively often. It's like the anime-version of Picard.
In The Movie, Itsuki does this in the background after a bit of Ship Tease between Kyon and Haruhi ( the hospital scene near the end of the movie). Doesn't happen often.
Lawrence does this quite frequently in Spice And Wolf for any given reason although usually in response to Holo. Holo herself has a half a minute long face palm in in the first OVA in response in response to Lawrence's description of how sheep are used for torture.
In Full Metal Panic!, several characters have been shown or described to have done this in reaction to Sōsuke's actions or outlandish conclusions. Most commonly done by Mao, Kurz, and Kaname.
In chapter 2, this is Mizorogi's drivers response when Mizorogi tells Yura that the reason he wants to scout her is because she "smells like honey".
In chapter 21, Mozorogi does this again in exasperation for having acted a bit immature to Yura.
In season 2 episode 6 of Girls Bravo, Koyomi does this upon realization that Fukuyama's about to have an Unsettling Gender Reveal dropped on him and he doesn't even know.
In chapter 5 of Sensual Phrase one of Sakuya's fellow band mates reacts this way when he states that he wants to use Aine in a music video. In chapter 7, another one of Sakuya's fellow band mates has this reaction at Sakuya's less than subtle remark of taking Aine to his room when she passed out from drinking too much.
Dragon Ball Z: In the Cell Games, Mr. Satan opts to fight Cell first and starts showboating in front of him. Then he decides to show off by breaking 14 of the 15 tiles he prepared with a karate chop to intimidate Cell. Kuririn faceplams at the sheer idiocy of the man.
Goku also does one after Vegeta breaks the punching machine at the 24th Budokai, which the rest of the group had been taking care to hit very lightly so as not to damage it.
Black Butler: Ciel in season 2 episode 3, when Sebastian has a moment of adoration over stray kitties and ignores the task at hand to do so.
Kuroko does the headdesk variation in A Certain Scientific Railgun when the usually-straightforward, no-nonsense titular character (who is also her crush) lure the gangmembers with innocent charm. The charm works though. Kuroko hits her head against hard objects hard enough to shake them, and she does it often enough to become a Running Gag. It's a wonder she doesn't suffer from any injuries.
Fruits Basket: Yuki does it at the end of this clip after Hatsuharu changes back from black Haru and asks why he's so exhausted.
Persona 4: The Animation has Yosuke doing one in response to Yu's drunken shenanigans in episode 15.
In Tiger & Bunny, this is Barnaby's reaction to Kotetsu's massively botched attempt at performing the simple act of picking up a dropped pen...accidentally kicking it into the path of an oncoming car in episode 5.
Otani of Lovely Complex does this in episode 24 after seeing Koizumi's Epic Fail at being a model.
Germany of Axis Powers Hetalia has done this on more than one occasion, usually because of something Italy has done.
Sharon of Pandora Hearts does this in the second omake when Gil is supposed to be making a soulful declaration to Alice to prepare her for womanhood but he just does it to Oz instead.
Kiniro No Corda: Hino in episode 15 during an argument between everybody about eavesdropping. Also, in the same episode Tsuchiura does this when Hihara gets mistaken for being Hino's boyfriend.
When Luffy accepts to escort Vivi to Alabasta in spite of the crew being on Baroque Works' deathlist, Nami facepalms in exasperation.
The G-5 Marines keep on badmouthing the Straw Hats because if they don't, they will start admiring them. They admit this as they begin to break down in tears while Tashigi laughs and Smoker face-palms.
Tomoe, Nanami's Beleaguered Assistant from Kamisama Kiss, will usually end up doing this at least once an episode, mainly because Nanami tends to act first and think much later.
