Greed's chimeras are subject to this, most notably the snake girl.
Later, when Heinkel (a lion chimera) is fighting Pride, Pride notes that Heinkel isn't even hesitating to attack someone who looks like a little boy. Heinkel says that his animal instincts are screaming at him to kill the "boy" before he gets killed first.
One of the Inuyasha movies has the title character fetching a stick.
Satsuki, the werewolf in Millennium Snow, actually fetches a stick thrown by another character.
In Tokyo Mew Mew, Ichigo gets infused with feline DNA and suddenly finds herself snatching fish in her teeth.
She also takes cat naps, much to her distress, especially when it happens in class.
Animals turned human or humanoid in Princess Tutu usually act like humans, but almost all of them have at least one tell. For the protagonist, it's a tendency to waddle when she walks.
Mr. Cat is the best example of this though. His cat nature usually emerges directly after threatening his female students with marriage.
In chapter 30 of Ratman, Unchain gets a variant. He has the power to absorb the DNA of things he consumes, which have mostly been normal and genetically engineered animals. When fighting Ratman, every single cell in his body screams that he can't possibly win, that Ratman is about a hundred steps higher on the food chain than him. Considering that he considered himself the top of the food chain (which is probably also where his name comes from), it's something of an ironic defeat.
In the Pokémon anime, Meowth of Team Rocket sometimes reverts to regular feline behavior. Though he's a Gadgeteer Genius who taught himself how to speak human language and walk bipedally, he can't resist a chasing a ball of yarn on all-fours or chowing down on a bowl of clams.
In Sam & Max, one comic story has Sam (a dog) incapacitate a crook by biting his arm. It works, but afterwards, Sam says to the audience that he's never done that before, and he's really embarrassed.
In the Cat People remake, the first time Irena comes close to transforming, she strips off and hunts a rabbit in the bayou. Earlier, when frightened, she leaps to the top of wall. Her brother Paul often climbs trees and after a transformation, will eat the leftover skin clinging to his body.
In The Black Cauldron, Fflewddur Fflam keeps getting turn into a frog and back again by witches. Moments after he's turned back to normal for good, he catches a fly with his tongue and eats it.
In Gremlins 2: The New Batch, one Gremlin drinks a brain hormone solution and becomes extremely intelligent. However, he is still as sociopathic as his fellows, even shooting another gremlin in the face just to make a point about civilisation.
Folklore & Mythology
One of Aesop's fables, "The Cat-Maiden" involves this. The gods Jupiter and Venus have a bet as to how much people can change themselves. They turn a cat into a human woman, and set her up to marry. Venus proves her point that "nature will out" by causing a mouse to run through the wedding ceremony, causing the cat-bride to embarrass herself when she tries to chase and eat it.
In Aesopus Emendatus, Ambrose Bierce does his usual piss-take on it by having the cat-turned woman not try to chase it, but rather to scream and carry on so much that the human she was falling in love with gets fed up.
Werewolves in Discworld have some doggy instincts even in human form. They tend to wince at the word B.A.T.H., for instance. Angua is the only one who tries to suppress these instincts.
Some Vampires have almost as much trouble, particularly with the reversed-names thing.
Played horrifyingly straight in Witches Abroad with the Big Bad Wolf. Lilith tried to "enhance" a wolf so that it would think and speak like a person... which left the beast a tortured mess torn between human logic and animal instincts.
Happens in the Animorphs series. Once, while morphing seagulls, they found it hard to maintain a train of thought because they kept greedily eyeing every dumpster with a half-finished bag of chips sticking out as they flew over.
Actually, happens at least once a book, what with it trying to be educational and teach kids about different animal instincts.
"Kill. Kill. Kill and eat." — a lobster brain
Then there was the wolf morphs. Jake was the alpha and couldn't stop himself from peeing every so often to mark territory.
On a related note: Marco, having anticipated dog morph to be pretty much the same as wolf form, was caught off guard by the domestic dog's urge to goof off. (And dogs, they want to have fu~un, Oh dogs, just want to have fu~un...)
Once Cassie was almost eaten by Tobias trapped in hawk morph when she morphed into a squirrel for the first time and was temporarily overwhelmed by its instincts as a prey animal.
Speaking of Tobias, one of his major character struggles is trying to maintain his humanity despite being trapped in a (fairly)-permanent hawk form.
The termites. At first they were fine, until they got near the hive and were hardly able to assert their will over over the Queen's control.
When they go dolphin, they often have trouble focusing because their minds are so playful. It still makes a good combat morph due to dolphins' ideas of fun.
Inverted in the Belgariad. A sorcerer who takes the form of an animal will find that they start to acquire that animal's instincts and some of its behaviour. This gets worse the longer you spend in that form, and as Belgarath notes when the time comes to change back to your natural form you might not want to. However, as a side benefit you instantly acquire the language of the species you change into and retain it when you change back, because all animal languages are the result of brain patterns not culture.
Appears regularly in David Brin's Uplift novels. Almost all Galactics - alien species that were genetically engineered by older species to give them sapience - have their own, unique forms of what they call "stress atavism." Great psychological stress causes these creatures to partially or totally revert to the instinctual behavior of their non-engineered ancestry. It's also seen among humanity's own "client species": the dolphins in Startide Rising suffer this fate to varying degrees and in varying forms, and it's a lesser plot point among the chimps in The Uplift War.
In Seraphina dragons are prohibited from eating meat in human form so their carnivore instincts don’t lead to unfortunate consequences for the humans around the table...
In A Wolf In The Soul, as his werewolf transformation gets worse and worse Greg starts doing insane things like eating raw meat right in front of his family.
Live Action TV
All the transgenics from Dark Angel are subject to this occasionally. Dog-based Joshua growls, snuffles interesting things, and acts like an excited dog around food; cat-based Max and Alec show varying feline behaviors like distrusting dogs, fastidiously bathing, acting predatory around prey animals, picking the people who least want to see them at the moment and sitting right next to them...
In Sanctuary, Henry can't help his pupils dilating when asked how he'd feel if he would smell the blood of a wounded animal in the woods, even if he answers he'd feel sad.
In Being Human (US) When Josh and Nora are "being together", Josh abruptly abandons ship after he accidentally growls.
In Faerie Tale Theatre's telling of "The Frog Prince", at the end the fully human prince is standing for a family portrait when a fly comes buzzing around. Cue his eyes tracking it and his tongue flicking out.
GURPS calls this Stress Atavism. Most templates for uplifted animals have it.
This is common in Changeling: The Lost, as shown in the Curses for changelings of the Beast and Elemental Seemings. Beasts spent so long as wild animals that thinking non-instinctively is hard for them, resulting in a penalty of rolls requiring Intelligence. Elementals, likewise, spent so long as a primal force that interacting socially with other humans is a rough affair.
Nick Bottom in A Midsummer Night's Dream is an especially funny example; he isn't aware that he's got an ass's head, he just knows that he's in the mood for oats, dried peas and a bottle of hay.
In the first act of Prince Ivan by Alexander Ostrovsky one of heroes wonders aloud why does he always want to meow when he feels sad. A stray cat hears him, turns into a human-sized bipedal cat woman and tells that she is his mother, who lost him some 20 years ago. (Later she turns out to be a cursed Oriental sorceress princess.)
In the Black Velvetopia level of Psychonauts, Raz gets the bulldog painter to help by asking "Who wants to go for a walk?" The painter struggles against, but gives in to his "stupid dog brain."
A brief example from the October 1st Nintendo Direct trailer for Super Mario 3D World (about 0:49 of the video): Mario, in his Cat Suit, is shown sneaking up on birds and trying to pounce on them.
In the RWBY episode "Burning the Candle", Blake can't resist following Yang's laser pointer. A few episodes later, she's the only member of Team RWBY to dislike the puppy Ruby and Yang's father sent.
Myan from Cat Nine still acts like a cat whatever form she takes. It's doesn't matter much if she transforms into something similar(like tigers) or if she transforms to a human/Cat Girl, but she's having trouble with her owl form.
Sam is prone to falling back on his scavenger-instincts too, claiming that "Food tastes better when you steal it from a predator", among other things (though often he does this deliberately).
Now, watch Sam and Florence's instincts crash into one another; what Florence the social predator sees as deferent behavior from a lower-ranking pack member is considered to be nigh-heroic alpha male behavior by Sam's species (provided you do it to your enemies; Sam got chased off his homeworld when a stunt like this got out of hand and ended up seriously inconveniencing his own royal family).
From Girl Genius comes Krosp III, Emperor of All Cats - basically, a cat with human-level intelligence, speech, thumbs, and the ability to walk erect... he'd like to claim that his 'cat-instincts' have no hold over him, but Agatha rather enjoys proving otherwise. Using a piece of string.
From the webcomic Tanktop, Texas: "I am a dog, should I pretend to be something I'm not?". Subverted in that the animals in this strip are quite the Intellectual Animals and he turned into his feral self deliberately, just to prove a point.
Seen in Tails The Douche, when Tails, after freeing the cute chickens from the Mystic Cave boss capsule, starts eating one alive.
In the rebooted Furtopia RP of Darwin's Soldiers, Captain Kayle Storm (an unspecified lupine soldier) Lampshades, subverts and plays this trope straight. When his rifle jams, he clubs a terrorist with it and latches his jaws onto the terrorist's face and proceeds to maul him. Subverted in the fact that he spends a few seconds vomiting after he does so.
Capt. Storm: Instinct. What a love-hate relationship.
Brian from Family Guy lives this; his family members even occasionally invoke the trope to distract and/or humiliate him. For example, he will chase balls, is attracted to the sound of dog food in a bag, and is terrified of the vacuum. He also has a tendency to bark at strangers, especially black strangers (subconscious racism due to his father, something he is very ashamed of). He will sometimes fail to recognize himself in a mirror, thinking it as another dog (though this only ocurred in a gag, followed by Peter doing a similar thing).
Probably best represented in an early episode where Brian goes off to see the world. We see him digging for fossils (with a trowel), uncovering a bone and being proud of his discovery. Then he immediately re-buries it (with his hands/paws) and sits on the spot, looking around to make sure nobody tries to take it.
Every now and again Stewie gets a "baby reminder" (being unable to see Peter when he covers his face with his hands, for example), just to point out that he's still technically an infant.
Stewie: Where the devil did he go?
Peter(uncovering his face): Peekaboo!
On Foster's Home for Imaginary Friends Mr. Herriman, a rabbit, has an addiction to carrots that he's ashamed of. Not to mention his fear of dogs, which is so strong that he calls out "Frankie" instead of "Ms. Francis."
A common gag in T.U.F.F. Puppy. Most often in the form of Dudley chewing his own butt. Kitty acts on her instincts much less often than Dudley, but give her a cat toy and...
The Chameleon often blows his cover because whenever he sees a bug he has to eat it.