In Animal Land, some animals walk on two legs and some walk on all fours. A number of them though zigzag between walking on two and four.
Meowth from the Pokémon anime learned to walk on two legs so that he could be respected by humans. In an ironic twist, this made him a freak amongst other Meowth.
Oddly though, Meowths have always been shown to be on two legs in their game sprites (albeit in stances like an actual cat or dog trying to walk or sit on their hind feet) and Meowths in future episodes are shown to walk on two feet. In the Gold and Silver remakes, Meowth's sprites depict them walking on four legs suggesting they aren't the best at two feet walking.
Also, the evolutions of some Pokémon that are quadrupeds assume two-legged stances when they evolve (and vice versa). Some are justified, such as Slowbro (as the Shellder that clamp onto their tails provide leverage to weigh them back). Generally, Pokémon that can assume a bipedal stance have better movepools then their quadrupedal cousins.
Very visible in the Garfield comics: the protagonist originally was drawn walking on all four, then switched to walking like a human as he came to be depicted increasingly human-like (to the point where he is hardly ever seen not walking upright these days). By comparison his pal Odie the dog still rarely ever assumes a two-legged stance.
Snoopy from the Peanuts comics, movies, and TV specials usually stands on two legs, except for the earliest comics.
Jim Davis of Garfield fame admits it was Charles Schulz who taught him how to design both four- and two-legged posture for an animal character.
Oddly in an early comic, he understands he loves Sally because she's the only human who knows how to walk on four legs.
And in an early strip we actually see the first time he walks on two legs "on-camera" rather than this being a background thing, with Charlie Brown trying to teach him to stand on two legs and Snoopy immediately getting the hang of walking on them.
The Far Side had quadrupeds walking upright as often as it had them on all fours.
The Barnyard example may have been Inspired By a Far Side comic where cows were standing up until a spotter shouted "CAR!" Then they went down to four legs when a car went by, after which they went back to standing.
Heathcliff was shown on two legs quite a few times. So were Belvedere and the pig in another Jim Davis strip, U.S. Acres.
Alex the lion, Gloria the hippo, and Maurice, King Julien, and Mort the lemurs from Madagascar usually stand on two legs, but Marty the zebra and Melman the giraffe would sometimes stand that way too.
Boog the Bear from Open Season usually stands on two legs. Elliot the mule deer also stands occasionally, which causes the hunter Shaw (who's already not all there to begin with) to utter the page quote in horror.
Tiana and Naveen as frogs and Louis the alligator from The Princess and the Frog usually stand on two legs. Louis apparently does it to play the trumpet properly.
Timon is the only character in The Lion King that walks on two legs (not counting Zazu, who, being a bird, is exempt from this trope).
The other meerkats in The Lion King 1 1/2 usually walk on two legs as well.
Truth in Television in that meerkats actually do stand like this in real life to scout their territory, but also Exaggerated because they never walk like that, only stand.
Two-legged Charlie B. Barkin from All Dogs Go to Heaven, a German Shepherd/Collie mix, contrasts with Itchy Itchiford, who walks on all fours because of his Dachshund anatomy.
Inverted in Tarzan, as the hero of the movie is a human who walks on all fours and generally behaves like a gorilla, owing to how he was raised.
Everyone from Rango is a biped except Rattlesnake Jake since rattlesnakes don't have legs, and the armadillo, who is a quadruped.
In general, the characters in Kung Fu Panda (those that fit this trope anyway) walk on two legs, but some switch to all fours when running, presumably just for the sake of speed.
In The Secret of NIMH, all the talking animals are bipedal, while the rats used to walk on all fours before escaping from NIMH. During the tractor scene, Mrs. Brisby alternates between the two.
Animal Farm: The Trope Namer. It's the central concept of the story: as Napoleon (a pig) became more tyrannical and corrupt, he ultimately abandons one of the most important characteristics that the animals took pride in because of how it made them different from the humans - the notion that four legs are good and two legs are bad - and decides to walk on two legs, like a human.
Retconned in the Spellsinger novels: in the first one, Jon-tom is informed that most hoofed mammals aren't intelligent, but later books show these quadrupedal warmlanders talking and using tools designed to be grasped with lips.
Walter Brooks' Freddy the Pig started out on four legs but in later books stood on two legs when necessary, such as when he pretended to be a midget during a certain detective case.
Most of the time, Donkey Kong walks on all fours except when he carries something like a barrel. In Donkey Kong 64, however, he always walks on two legs, yet still has the typical posture of a gorilla when he's just standing.
In both Jet Set Radio games, Potts the Dog stands on all fours...until you unlock him as a playable character.
Final Fantasy VII plays with this with a sequence on the Junon Cargo Ship in which Red XIII is in disguise as a human and has trouble standing on two legs. The theme for the Cargo Ship, which has a somewhat comic feel, is translated variously as "It's Hard to Stand on Both Feet!" or "It's Difficult to Stand on Both Feet, Isn't It?"
In the Disney adaptation of The Wind in the Willows, Cyril Proudbottom the horse sometimes stood on two legs, but Mr. Toad, Ratty, Mole, Badger, and the weasels always stood on two legs.
All of the animals in Slacker Cats walk on their back legs but the wild tiger they find doesn't (he also doesn't talk) because he's more in tune with his wild side than they are.
Both Ratty and Mole from Mr. Bogus walk on two legs.
In The Simpsons Bart once got an elephant, and the family was concerned all the time with it. The cat and the dog try to do anything to call the Simpsons' attention... including to stand in two legs and say that they love them. They fell to the ground one second afterwards.
Dinosaurs. They're the first bipedal vertebrates known in history.
At least, the theropods are.
This is generally best done by plantigrade mammals, such as apes, baboons, capuchin monkeys, giant pangolins, bears, and the extinct ground sloths, while digitigrades like dogs, rabbits, and cats are generally a little less capable of this and unguligrade animals like horses and cows even less capable of this.
Most mammals that are bipedal, like kangaroos, wallabies, jumping mice, kangaroo rats, jerboas, and springhares, hop bipedally rather than walk that way, and sifakas and indris stand and leap on two legs.