Mickey Mouse's classic look has red shorts with gold buttons, but no shirt. And note that it's only his "classic" look where he counts as this. Every other outfit Disney's put him in has a shirt.
When Goofy first appeared (as Dippy Dawg), he wore only a hat, vest and shoes (along with the prerequisite White Gloves). Of course, he eventually became fully clothed after being given a more human-like appearance at the start of the color film era.
Most of the Disney duck characters are both pantsless and unshod, but Scrooge McDuck wears spats on top of his webbed feet.
Ditto most of the duck characters in Darkwing Duck (which was explicitly set in the same world). Including Gosalyn, unusually, although not including Morgana. Morgana was more humanoid, though.
Launchpad and Mrs. Beakley were also exceptions to the pantsless duck rule, normally appearing fully clothed, although Launchpad on a couple occasions dressed in the costume of Darkwing Duck, an outfit that included neither pants nor shoes.
Although a typical pantsless duck, Darkwing was at times bizarrely shown to have boxer shorts beneath his costume, which was way too short to cover such a garment.
Another pantsed duck would be Quackerjack, with his jester outfit.
Daisy Duck was another exception to the shoeless duck rule. (And the cast of the animated Mighty Ducks series were always fully dressed, but they inhabited a more realistic universe. Well, as realistic as a universe with giant anthropomorphic hockey-playing ducks and villainous alien dinosaurs voiced by Tim Curry can be.)
The normally bottomless Donald Duck nephews Huey, Duey, and Louie were given shorts when they were redesigned as preteens for Quack Pack.
The legend is probably based on the few angry letters that the Finnish Donald Duck magazine received decades ago on the subject, and responded by publishing a picture of a ridiculous-looking duck with pants, which largely killed the issue. Many Finns find this legend amusing, in that the nudity taboo is far weaker in Finland than it ever has been in America, and there have been several comics in the country's national newspaper which have on occasion showed naked characters with visible but non-pronounced genitals, leading to no repercussions.
There's also the fact that Donald Duck is the most popular fictional character of them all in Finland. That would be an even bigger achievement were he banned.
Mickey and Donald being half-naked was played with in one of the recent Disney Channel shorts. Donald and Mickey want to buy food, but the store owner refuses to sell it to anyone with no shirt or pants. The short ends up being the two fighting to get the other's piece of clothing.
Minnie Mouse and Clarabelle Cow featured designs which had skirts and underbloomers, but not necessarily shirts. In more recent years, however, someone apparently decided that wasn't acceptable and changed her default outfit to a dress. Since then, depictions of her in the red polka-dotted skirt have been mainly limited to the Mickey Mouse Works-era cartoons, and depictions of her white-faced, black-eyed "classic" design.
Minnie's earliest cartoons (Steamboat Willie period, 1928-29) had her wearing a bra over her naked chest, but from late 1929 she went completely topless.
The decision seems to have been made to treat Mickey's and Minnie's black fur as an item of clothing itself. In The Grocery Boy Minnie momentarily pulls back the fur on her chest, showing us that she keeps her powder puff underneath!
Daisy Duck is rare among female characters, as her bottom half is normally uncovered.
Roquefort the mouse from The Aristocats is usually naked, but is occasionally seen wearing a hat and coat at times.
In Bonkers Bonkers D. Bobcat and most of the other anthromorphic male cartoon animals wear only shirts, while female cartoon animals wear skirts or dresses.
Chip 'n Dale Rescue Rangers lampshaded this trope: In the Body Swap episode "A Fly in the Ointment", the usually jumpsuit-clad Gadget is bodyswapped with the pantsless Dale. Upon noticing "her" "nudity", Gadget immediately fashions a makeshift skirt from a Dixie cup which "she" wears for the rest of the episode.
Timothy Q. Mouse and the crows from Dumbo are pantless, but the stork is more or less fully dressed.
Hyacinth Hippo from the "Dance Of The Hours" segment of Fantasia.
Both Waternoose and Roz from Monsters Inc. Besides those two, Celia, maybe a couple other females, and the grocer and octopus (both in aprons), everyone else runs around stark naked (fur and general reptile/amphibian/fish/insect anatomy rules cover them).
The anthropomorphic cast of Disney's Robin Hood film follows the bottomless male/fully-clothed female rule. Possibly because a medieval tunic/jerkin with no trousers looks a lot less risque than a medieval peasant blouse/corset with no skirt.
In "Vowel Play," the "skywriting" episode of Disney's TaleSpin, the normally pantsless Baloo's shirt comes off as well, resulting in a naked Baloo (wearing only a hat). Rebecca Cunningham, his Barefoot Cartoon Animal female boss, proceeds to berate him... but only for his spelling errors.
In a later episode, "My Fair Baloo", an episode in which all the attendees at a formal ball strip off their outer garments to sew them into a giant hot-air balloon in order to fly the massive airplane that had served as the site of their dance home, Baloo has on an undershirt.
That doesn't even cover the half of it, so to speak. The tuxedo that Rebecca rented for Baloo originally had a pair of pants before he puts it on.
Another TaleSpin episode ("Plunder and Lighting", the pilot) featured Rebecca being repulsed by dirty socks on Baloo's bedroom floor. One has to wonder where these socks came from, considering Baloo, as well as most of the rest of the show's cast, went barefoot. (Rule of Funny probably explains it.)
Roger Rabbit from Who Framed Roger Rabbit wears red overalls, and a blue and yellow bowtie. Only one of the weasels wears pants, and for some reason he hikes them right up to his chest. (Possibly because weasels have low waistlines and short limbs, so this is the only way he can reach the pockets.)
The Disney version of Winnie the Pooh wears a shirt with no bottoms. It should be noted that in the original book illustrations, Pooh only wore the shirt during winter, going au naturel otherwise.
Abby Mallard from Chicken Little, which was somewhat strange considering that the majority of the rest of the cast either wore full costumes or nothing at all (with the possible exception of Fish Out Of Water, but his helmet was for breathing, not really for fashion).
That's Peter and Bobby Farrelly, by the way. Who would totally do that.
A Boomerang short plays with this where a bunch of cartoon characters can't buy anything at a store because of "No shirt, no shoes, no service." So Quick Draw McGraw, who is wearing horse shoes, takes Fred Flintstone's shirt and asks to buy clothing for the rest of the toons, the shopkeeper responds, you need pants too. Quickdraw's usual outfit consisted of a red hat, a blue bandana, and a gunbelt; El Kabong wore a black hat, a bandana-style mask and a cape, and Baba Looey wore a yellow sombrero and yellow bandana.
In a lot of the older Donald Duck cartoons, Donald's modesty is played like a fourth wall joke; he walks around without pants all of the time, but whenever his shirt gets removed he immediately covers his crotch.
Lampshaded on The Looney Tunes Show episode "Jailbird and Jailbunny" when people keep pointing out that Porky Pig has no pants, and Porky seems embarrassed enough to buy a pair. Funny how they never notice that Bugs and Daffy are completely nude.
However, Bugs has fur and Daffy feathers. Pigs have relatively little hair on their bodies compared to other mammals like rabbits.
Note that, at least in the most recent incarnation of the series, no one points out that the TMNT are mostly naked; so, even though they can't take off their shells, the shells could possibly be considered clothes in the barest sense of the term.
The Seville brothers of The Alvin Show and Alvin and the Chipmunks didn't wear pants because (until the 2007 franchise reboot) their turtleneck shirts were long enough to reach their ankles.
The Chipettes are a different story altogether. In the 1980s cartoon they were always fully dressed. Early promotional material for Alvin and the Chipmunks: The Squeakquel seemed to suggest they were going to wear skirts over their naked lower halves. In the final film the girls wear shirts, and skirts that obviously don't reach that far down, and it seems like the Chipettes make only a half-assed attempt at being fully clothed as it leaves their butts visibly unclothed. So, first they are fully clothed, then implied to be half naked, then go obviously half naked...
Where to begin on Animaniacs? Yakko wears pants but no shirt. Wakko wears a shirt, but no pants. Dot wears a skirt and bloomers but no shirt. Walter Wolf wears overalls, a hat, and yellow gloves. Rita, Skippy, Slappy (she only wears a hat), Pinky and the Brain prance around in the nude with pride, but if Minerva Mink ever did the censors would be up in arms!
In Wakko's Wish, Skippy is wearing a shirt without pants (at least in the wintertime).
Yakko Warner wears tan pants with a black belt and White Gloves.
Wakko Warner wears a light blue shirt, a red baseball cap, and White Gloves, but no pants.
Dot Warner Dot wears a pink skirt, bloomers, and White Gloves, but no shirt.
Wilford B. Wolf wears pants, glasses, and a bowtie,... but in Fabio-esque form, he wears torn shorts and a bowtie.
Walter Wolf wears overalls, a hat, and yellow gloves.
In contrast to Walter Wolf, his female nemesis Slappy is usually seen wearing nothing but her hat. However, she was fully clothed in "Hurray for Slappy" and "Macadamia Nut" (except for the shoes, that is), but otherwise, if Slappy decides to wear clothes (in episodes like "I Got Yer Can", "Critical Condition", "No Face Like Home", "Mighty Wakko at the Bat", "Soccer Coach Slappy" and "Sunshine Squirrels"), Slappy wears a shirt and no pants.
Wakko: This is a bit much.
Dot: I'll say.
In The Backyardigans, Pablo's regular garb consists of nothing but a blue and yellow propeller beanie and a blue bowtie. Tyrone wears an orange and blue striped sweater with no pants, yet is still often seen with his hands in his pockets for some weird reason. The other three members of the cast (no other characters are ever seen, heard or even mentioned) are pretty well covered with Tasha being the only one of the children who wears shoes.
Most of the cast of Camp Lazlo are half-dressed.A notable exception is the episode where Edward goes around pantsing everyone, where suddenly everyone is wearing pants. The fact that Edward himself gets pantsed in the ending scene is spoiled by the fact that he himself wasn't wearing pants until that scene.
In Chowder, the title character is apparently wearing pants, he's just so fat that his poncho/shirt mostly covers his shorts when he wears it. However, the animation isn't very consistent, and he'll occasionally be shown wearing nothing else under it.
Also, Shnitzel tends to wear nothing but an apron and underpants a good percent of the time.
Lampshaded on the "Once Upon a Tyne in NYC" episode of The Cleveland Show as Cleveland rescues Tim the Bear from a gay bar.
Cleveland: He's not interested! Gay Barfly: Then why did he walk into a gay bar without pants on?!? Cleveland: Cartoon bears NEVER wear pants!
In "You're the Best Man, Cleveland Brown," everyone goes to a strip club and Tim just finds the most out-of-the-way corner to get drunk...because a strip club is a bad place to be when you don't wear pants.
The Fosters Home For Imaginary Friends episode "Adoptaclypse Now" had a brief scene where it's pointed out that most imaginary friends are nude... and then Mr. Herriman freaks out over not wearing pants. He proceeds to hop around in too-big pants for a good duration of the episode.
Though Bender from Futurama isn't an animal, he goes around naked most of the time. He will, however, occasionally become modest and wear a towel or some other form of covering as the situation requires, like when he and Fry were relaxing in a steam-filled room.
Another Futurama example: Kif Kroker runs around in the tunic-cum-uniform without pants that Zap Brannigan imposed on the Earth military, but while Zap and all the humans are carefully covered, Kif's underwear frequently shows, between his lackey role, alien anatomy and ability to climb walls like a gecko. One bizarre way this is used is when he peels off his skin with his uniform (and precious ambergris) on it, revealing a new naked skin below, that is somehow wearing underwear.
This gets even stranger when you realize that Kif's species reproduces through any skin contact, meaning he would not realistically have or need genitals.
In Happy Tree Friends, most of the characters wear no clothes, but Pop does wear a smoking jacket and Cub wears a diaper, and Flippy wears an army jacket and cap but no pants. Lumpy apparently doesn't wear anything either, but in one episode he was seen wearing a towel and ironing a shirt and pants the exact same colour as his body, his nipples and butt were visible, and Giggles screamed when he opened the door to see her and his towel blew away. Disco Bear is the only fully clothed friend as he wears a disco suit.
Various animal characters from Hoodwinked including the Big Bad Wolf, Boingo the bunny and Twitchy the squirrel. The Wolf initially wore a blue hoodie in the first movie, and later added pants to his wardrobe for the sequel.
Po, Tai Lung, and Master Monkey from Kung Fu Panda all wear shorts, but no shirt. as does Master Crane.
Leo Lionheart, the main character of MGM's The Lionhearts series, wore just a sweater. His dad, Grandpa Lionheart, wears a sports jacket.
Tweety Bird was pink in his early appearances, depicted as a naked newborn chick. Warner censors said that it was unacceptable, and there was talk of putting pants on him. Instead, animators went with yellow feathers, and made him a canary. He did wear a small sailor's cap for a while, but he soon lost it.
The female gorilla from the Looney Tunes cartoon "Apes of Wrath" wears a pink skirt that looks just like Dot Warner's skirt.
Subverted in the road runner episode "War and Pieces." Wile E Coyote (who never wears anything but a crash helmet) builds a longbow device which rips the fur and skin off his legs. Underneath, he's wearing polka dot boxers.
Heavily played with in My Little Pony: Friendship is Magic, where clothing of any sort is a formal item for ponies, and as such runs the gamut from minimal to deeply covering. In Canterlot in particular, it seems that almost everyone wears some clothing, which makes sense since it seems to be populated by upper-crust folk.
Lampshaded in "The Best Night Ever" when the ponies are getting ready for the Grand Galloping Gala:
Spike: Come on, you guys! Let me in!
Rainbow Dash: Sure thing, Spike!
Rarity: Heavens, no! We're getting dressed!
Applejack: Dressed? Uh, beg pardon, Rarity, but, uh... we don't normally wear clothes.
Rarity:(groans, opens the door) Sorry, Spike. Some of us do have standards.
Not to mention in "The Super Speedy Cider Squeezy 6000", when Rainbow Dash yanks the covers off Fluttershy, and Fluttershy immediately covers her non-existent breasts with her front hooves while blushing furiously.
A commonly told joke among bronies is that Ponyville is a nudist colony.
So far, Rarity's mother seems to be the only pony to actually wear pants with her shirt.
The Mouse King from The Nutcracker Prince movie is considered this trope as he wears a cape, a crown and an armor plate.
Ludwig the bat from Pearlie wears a pair of glasses and a necktie.
Played with in The Pink Panther cartoons, where occasionally, the Panther would "undress" (typically just removing "socks" just before going to bed), but he looks exactly the same.
While the male aliens all wore only shirts (and no pants), the female aliens all wore shirts in addition to dresses and skirts. However, they still went barefoot. While this was supposed to indicate their society and thus their mode of dress was similar to America during the 1950s, it really just raised unpleasant speculation on the anatomical differences between the males and females.
In The Raccoons, all the males are nude or shirt-only. Melissa Raccoon wears only a shirt as well, which is somewhat strange as she actually has breasts. Lisa and Sophia are the only fully dressed main character in the series.
In Rango, the main character's regular duds consist of a red tropical shirt. There are a few supporting characters including Wounded Bird and Waffles the horned toad that apply to this trope as well.
Most of the other (anthropomorphic) animals are either fully clothed or Accessory Wearing Cartoon Animals. Rango gets a new outfit that includes pants before too long and remains fully clothed for the rest of the movie.
Edmund from Rock-A-Doodle, upon being transformed into a cat by the evil Grand Duke of Owls, starts out naked when he is rescued by the other animals, but he immediately had to put on a shirt and a hat because everyone else was wearing clothing, and only he isn't.
In Rockos Modern Life, most of the cast is fully clothed except for Rocko, Slippy the Slug, and the chameleon brothers, in Rocko and Slippy's cases they only wear shirts but sometimes if Rocko loses his, he will gain a pair of underpants, and if it's for a formal occasion Rocko will wear pants. The Chameleon brothers are naked and no one ever comments on this.
The Secret Of NIMH - The film that launched a thousand furries. Pretty much every character. There is even a scene in the third act where Justin suggests to Mrs. Brisby that she remove her cape (the only thing she wears) so that it won't 'get caught on something.' The scene unintentionally turns Justin into a pervert in the eyes of some fans.
Three and Four from Seven Little Monsters. Although having just an oversized T-shirt as his regular wardrobe, Three dons a different costume pertainable to the plot of each episode, in which case a good one-third of his wardrobe applies to this trope. Four sports a yellow T-shirt and purple top hat.
In Space Goose, Space Goose and Ugly wear only shirts (not counting Goose's space helmet). Sally wears a dress and boots, while Joe wears a shirt and pants. Dr. Donkey wears a top hat, a monocle and a dinner jacket.
In SpongeBob SquarePants, Mr. Krabs and SpongeBob are the only fully clothed males. While most females wear clothes, most of the males wear only shorts or bikinis, and Squidward only wears a shirt. This last is lampshaded many times; in one example, SpongeBob asks Squidward why he never wears pants, and at the end, he is seen wearing a pair; in another, he runs out of his house, wearing only bubbles over his private parts (with characters covering their eyes as he runs by), and at the end of the episode, SpongeBob gives Squidward his clothes to wear just before the last bubble, which is placed where his crotch would be, pops.
Plankton, on the other hand, is completely naked. This is pointed out in the episode where he switches lives with Mr. Krabs and is wearing his clothes, while Mr. Krabs goes around naked, to everyone's horror.
The "Silly Songs with Larry" segment in the Veggie Tales episode "Are You My Neighbour?" features Larry the Cucumber, fresh from a bath, wearing nothing but a towel wrapped around his waist. Repeated mention is made of how embarrassing it is for him to be meeting people in this state of undress — even though he's actually better covered than usual, since like most of the Veggies he normally wears nothing at all.
Cindy Bear from Yogi Bear cartoons wears a blue skirt, a yellow scarf on her neck, and a flower in her hair. She wore a hat in the original 1961 cartoons and in a few of her later appearances as well.
Clothing was a major plot point in the short Boo Boo Runs Wild.
There are other Hanna-Barbera characters who are half dressed, including:
Augie Doggie, Doggie Daddy's son (turtleneck)
Ding-A-Ling Wolf, Hokey Wolf's sidekick (bowler hat, short-sleeve shirt and vest)
Harvey Birdman, Attorney at Law had fun with this trope by portraying Secret Squirrel as a flasher (since he only wears a trenchcoat). Later episodes show him wearing boxers underneath after the court ruled against him.
Between the two title characters of Lenny & Sid, the former wears only a shirt, and the latter wears only overalls.
Skips the yeti from Regular Show wears only jeans and a belt to them.
Mr Bogus only wore a pair of blue shorts as his normal attire, except for a few occasions where he does become fully dressed, such as when he becomes his superhero alter ego, Super Bogus.