Rafiki does a depressed one in the sequel after he sees Simba exiling Kovu.
In Shark Tale, Don Lino does this and says, "Oy vey." in annoyance at his henchman Luca putting the record on the wrong song, which was "Baby Got Back (I Like Big Butts)" by Sir Mix-a-Lot. Frankie also does this.
In the first film, Beth groans and facepalms herself while in Gordy's police station to confront Shaw.
In Open Season 3, Gisela and Giselita do this sometimes (and at the end, they do a two-handed facepalm together as the ladies are starting to dance with Ian, who is their coach). Stanley also does this after Roger says, "It's destiny!" when the pets come to save Boog from the Maslova Family Circus.
Lord Victor Quartermaine: How on earth would those tiny-minded buffoons ever catch such a big rabbit? Lady Tottington: Mr. Wallace? Wallace: Um... with a big trap! Gromit:(facepalm)
Even funnier when everyone in attendance (minus Gromit) says stuff along the lines of, "THAT'S BRILLIANT!"
There's also Victor doing this after PC Mackintosh says "the beast [were-rabbit] isn't actually dead yet?!" with a megaphone. It's even funnier while said character is doing the gesture, the said officer said "oops" with a megaphone.
Towards the end of Disney's adaptation of Alice in Wonderland, during Alice's trial, unbirthdays are brought up, which causes a whole new party, and of course the Mad Hatter and the March Hare have to sing "A Very Merry Unbirthday to You" for the Queen of Hearts.
Dr. Faciller pinches his nose after his gang of evil shadows takes a severe beating from a firefly.
Disney apparently likes this trope; it happens thrice in Treasure Planet. The best one is Silver and Jim doing one simultaneously, then just...looking at each other.
The Nightmare Before Christmas: Jack facepalms himself after Lock, Shock and Barrel bring back the Easter Bunny instead of Santa (who Jack calls "Sandy Claws") and start fighting over it.
In Toy Story 3, a 17-year-old Andy does one of these when he believes his slightly aged mother has thrown out his toys.
Woody does one when he finds out Buzz thinks he's a Space Ranger again.
Done by The Carpet, of all characters, in Aladdin; especially impressive, as it doesn't have a face or a palm. Immediately followed by Aladdin himself, as he's trying to explain to Jasmine why he lied to her about the first time they met. Even Genie does it in the same scene. Well he hits his head, but still, it counts.
In Bolt, one of the mooks gets zapped when trying to facepalm with electric glove.
He's particularly prone to the "depressed" type doing it in the prologue, (wrapping both arms completely around his head in an effort to hide himself), and a few times in the mid-quel "The Enchanted Christmas."
In Finding Nemo, Crush does this when Marlin says he needs to get to the East Australian Current. "You're ridin' it, dude!"
Before they meet Anya, Dimitri and Vlad are holding an audition for girls to play Anastasia. One prospect is a middle-aged woman, who says in a sultry voice, "Granmama! It's me, Ana-STASIA!" Their reaction is a combination Head Desk and Face Palm.
Mulan: Mulan does this along with saying "Oops..." after the matchmaker calls her name and she yells "Present!" leading to the matchmaker saying "Speaking without permission..."
Kenai does this in Brother Bear when he realizes he has no choice but to escort Koda to the Salmon Run. But he goes with it so he could become a human again.
One is shown in Wreck-It Ralph when Vanellope learns how to drive. Ralph is trying to keep a safe distance from her so her car doesn't hit him. When Vanellope's car hits a stalagmite, Ralph does a facepalm as it falls down on him.
A mass one occurs in The Swan Princess. Princess Odette and Prince Derek are expected to go through an Arranged Marriage but because the idea was formed while they were kids they started to hate one another after being forced to spend multiple summers with another. However, upon seeing one another as adults they instantly fall in love and Derek announces to start the wedding. Odette isn't too keen on this and asks Derek why the rush. Derek responds it's because he thinks Odette's beautiful. Odette is flattered by the compliment, but wants to know if that's the only reason Derek wants to marry her. Derek responds "what else is there?" His mother promptly started crying and everyone else groaned at Derek's sheer lack of tact.
Lord Rogers: You should write a book. How to Offend Women in Five Syllables or Less.
Chicken Little. The coach of the baseball team the title character is on does this when Chicken Little swings the bat when he was just told not to.
Kirby also does this after trying to explain to Buck Cluck multiple times where his parents are, of course it doesn't help that all he speaks is gibberish.