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.
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 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.
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.
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.
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.
A non-comedic version of this happens when The Staff of The British Library do this in the Read or Die OVA in response to losing an entire squadron of troops due to a transport chopper crash while trying to kill the I-Jinn.
Sailor Moon Crystal Act 3 features a scene where our heroine is fighting Jadeite while Rei (who hasn't awakened as Sailor Mars yet) is watching. Rei has previously seen Sailor Moon out of costume, and instantly recognizes her: