Germany of Axis Powers Hetalia has done this on more than one occasion, usually because of something Italy has done.
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.
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.
This is Kanade's reaction at the end of Chapter 12/Episode 4A of Castle Town Dandelion, after Akane accidentally flashes her schoolmates.
Early on, Shirai Kuroko, a young girl law-enforcer, crouches and buries her face in her hands, appalled at the sight of her good acquaintance (later properly introduced as the series' lead) high-kicking a vending machine to make it cough up a free canned drink right in front of her. No, not because of all the law things and how the two were discussing those right up to that moment. It's just that the resulting upskirt shot provokes a complaint from Kuroko how unrefined, unladylike the other girl's taste in underwear is.
Kuroko does the headdesk variation, when the usually-straightforward, no-nonsense titular character (who is also her crush) lures 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 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. Krillin 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.
In Resurrection 'F' and Dragonball Super, Whis's response to Goku getting shot in the back because he dropped his guard is a facepalm, because this is exactly what he warned Goku about earlier in the story.
Durarara!!: This is Tom Tanaka's default reaction when someone (usually the person he's getting to pay their debt) pisses Shizuo off.
Rin in Fate/stay night does this a lot. She even has a number of different kinds of facepalms.
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.
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.
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.
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:
Rei: Are you... Usagi? Moon: No, I'm not! I'm not Usagi! (Luna, being an advisor in cat form, facepaws)
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.
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 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.