Cartoon cats who see Circling Birdies sometimes swat at them as though they were real.
It is definitely easier to list those Looney Tunes shorts that don't use this trope. Among those that do:
In "Daffy Goes Hollywood", Daffy Duck tries to get past a studio guard in order to see movie stars. At the end, the guard decides to help him see the stars — by hitting Daffy over the head with his nightstick. Daffy then calls the "stars" by name: "There's Alexis Smith, and Dorothy Lamour (a star in a sarong!)... Sufferin' succotash! It's Ann Sheridan!" and even gives one a kiss.
In "Rabbit Hood", Bugs Bunnytricks the Sheriff of Nottingham by telling him that the king is coming, and then hitting him over the head when he turns and bows. The Sheriff then sees little kings walking around his head, leading to the classic line, "Odds-fish, the very air abounds in kings."
The Road Runner short "Going! Going! Gosh!" has Wile E. Coyote getting run over by a truck, then having little miniature trucks circling his head in place of birds or stars.
In "Baseball Bugs", one of the Gashouse Gorillas is knocked out, and surrounding his head are four little baseball players with angel wings, tossing baseballs among themselves.
In "Yankee Doodle Bugs", Bugs visits Betsy Ross to check on the progress of the new U.S. flag. Feeling the blue field is too plain, he paces around the lawn trying to think of something to "snap it up a bit"... and carelessly steps on a rake. Pointing to the resulting stars orbiting his head, he asks, "Hey, Betsy, does this give you an idear?"
"A Pizza-Tweety Pie" definitely satisfies the "cartoon cats" criterion above.
In The Simpsons "Treehouse of Horror" version of The Raven, Homer runs into a wall and falls down with tiny Bart Ravens circling his head saying "Nevermore! Nevermore! Nevermore! Nevermore!" Bart himself experiences this trope in a later "Treehouse of Horror" spoof of Nightmare on Elm Street. In his dream, after being hit with a Frisbee, birds circle his head while "No Sale" signs pop up in his eyes.
Also seen in the Season 20-present Couch Gag, in which Jebediah's statue's head falls on Ralph's. One of the things he says after being hit is, "I see stars!"
In A season 26 episode, Maggie befriends some animals and recruits them to save an opossum from a dog. During the fight, a bird knocks the dog away, and the dog sees circling chirping birds around his head. But then the dog hits back, and the bird ends up seeing circling barking dogs around his head.
Dragon Booster: The title character comedically falls down a pipe, and when he hits the ground, a bunch of curvy stars — his personal emblem — circle his head.
In the Spongebob Squarepants episode "Survival of the Idiots", Patrick gets hit in the head and sees chicken drumsticks.
Lampshaded in "Daring Don't"; when Rainbow runs into a tree where Fluttershy is helping some baby birds in their nest learning to fly, the chicks fly and circle around Rainbow's dazed head.
Clover gets the spinning stars and planets with the sound of chirping birdies variant in "The Play's the Thing" on My Little Pony Tales while being spun around in a barber's chair.
Lampshaded in Tiny Toon Adventures, where animal lover/killer Elmyra gets trapped in the mall after closing time. At one point she gets hit on the head, send birds flying around her head. Then Elmyra grabs one of the birds and hugs it, which also has smaller mini-birds circling around its head.
Normally in the Teen Titans cartoon, Blank White Eyes are used. However, circling stars were used in the episode "Switched" when Puppetmaster-controlled Robin accidentally hit himself with his own baton.
Used much more frequently in the decidedly more cartoony series "Teen Titans Go!"
In the Super Mario World cartoon, Mario gets hit in the head while trying to find something useful in the blocks. Due to this, when he does find something (a feather), he's too dazed to be able to catch it. He then grabs one of the stars circling his head, and is able to use it as if it were a Starman powerup.
It also happens on the The Super Mario Bros. Super Show episode "Pirates of the Koopa", when Mario asks for a star which is circling the parrot's head after he bumped it on the top of the crow's nest.
Played with in the Pixar ShortDay and Night, whose characters have scenes visible inside them. When Day gets hurt, birds are seen flying inside his head.
The cartoon versions of Chris and Martin Kratt often experience this in their animated series Wild Kratts. The circling creature usually corresponds to whatever critter they're following that day. For example, after a fall from a tree in one episode, Chris sees circling lizards. Another episode features Chris seeing circling walruses and Martin seeing circling polar bears after a blow to the head.
In Aladdin: The Series, in the episode "Never Say Nefir", flying rhinoceroses circle Aladdin's head after he's hit with a tranquilizer dart.
The title character of American Dragon: Jake Long experiences this frequently. In one instance, he sees tiny versions of his dream girl Rose running around his head after being knocked silly by a locker door. Jake's buddy Spud sees circling fish in another episode after a chair the throws boomerangs back on him.
Done all the time in Ed, Edd 'n' Eddy, but was invoked in "The Luck of the Ed", when Ed was trying to recount what happened when he lost Eddy's magazines:
Ed: Then I hit my head on that branch— (Ed smacks into a tree branch, then walks around to the other side of the tree) Ed: Nope. Sorry. It was this one. (Ed smacks his head on the other tree branch.) Ed:Then I gazed at the stars...
Eddy's Brother has circling stars when he's defeated.
A Cartoon Network channel bumper/ident involved the Eds running at and into each other. As they fall down, a star appears above each one of their heads, and Ed remarks, "I see stars..."
Frequently happens in Adventures of Sonic the Hedgehog and was invoked in the episode "Tails Prevails" by Tails, who is at a junkyard searching for items to be used a gift for Sonic. After an unstable pile of junk falls on his head, the resulting circling birdies prompt Tails to remark that he needs to add wings to Sonic's gift.
Played with in the American Dad! episode "Home Adrone". Stan tosses a young man from a moving vehicle during a Chinese New Year parade, and after rolling down the street, the man sits up with tweeting birds, stars and other assorted objects circling around his head. The shot then zooms out to reveal the a boy is spinning a mobile above the man's head and blowing a whistle to make the bird sounds.
In Kid vs. Kat, this trope was experience in some episodes; however, Kat (aka Mr. Kat) has experienced this in some episodes being the only ones with Kat with the trope; for example, in Never Cry Sheep, when Coop slams a trash can on Kat, Kat has stars circling his head.
Used several times in the New Kids on the Block cartoon series. In this episode, when Jonathan is knocked out by a falling surfboard, he hears tweeting birds and sees tiny surfers around his head (he then develops amnesia and thinks he's a pro surfer). After Donnie is thrown from a horse, he sees miniature versions of himself on horseback circling his head. The New Kids' bodyguard Bizcut sees circling music notes when dazed in another episode. In this episode, Danny hears tweeting birds after a hard fall.
The Care Bears series used this trope frequently, especially in the Nelvana episodes. Beastly, Grumpy Bear, Braveheart Lion and Champ Bear were its most frequent victims, but most of the bears and Care Bear Cousins experienced it at one point, as did one of the kids the bears were trying to help. The show usually used stars but sometimes threw in other circling objects, most notably when No Heart saw circling bats after being knocked out by Grumpy.
In the old cartoon Spy vs. Spy episode, "Beach", a bird circles the black spy's head after running into a wooden stake (in which the white spy was able to get a photo from a woman to trick the black spy into running into the wooden stake.)
Also happens in "Wall", in which the white spy gets circling stars after getting smacked by a fence. (Strangly enough, stars also circle the hand at the begining of the episode when the white spy punches the brick wall.) Also, in "Basketball", at the begining of the episode, the black spy enters the scene in which the white spy notices the black spy and screws up, in which, as a result, the basketball hits the white spy in the head. Bird sound effects then play, as the white spy staggers in a daze, right before the black spy steals the ball. Also, in "Toliet Plunger", the white spy sees circling birdies after a hit to the head with a toliet plunger, with a rock attached to it to make it look like as if it were a HAMMER.
On Futurama, the sign in front of The HAL Institute for Criminally Insane Robots has birds circling above it.
In the Futurama Holiday Spectacular, Fry sees spinning Christmas, er, Xmas ornaments after Robot Santa clubs him with a candy cane.
Eminem — in his "normal" form of Marshall Mathers, rather than his Slim Shady alter ego — sees circling birdies with a side dose of a Cranial Eruption after being thrown from a mechanical bull in the second episode of his animated series "The Slim Shady Show."
In Dudley Do-Right episode "Flicker Rock", Snidely Whiplash pushes a big rock down on Dudley's head with no effect of killing him, but causes Dudley to deal the episode of seeing things like birds and trains that aren't there.
The title character of Zekes Pad sees circling pancakes twice after mishaps during gym class in the series's first episode. Zeke had eaten a lot of pancakes for breakfast, resulting in numerous slips and falls during gym.
It happens to Bogus once again in the second act of the episode "Waterboy Bogus", after Running into the Window trying to get into the penguin exhibit, but sees penguins circling his head.
In the Total Drama Island special bridging the first two seasons, birds circle Courtney's head after she slams into a camouflaged wall. She shoos the birds away, prompting one of them to angrily chirp back at her.
Mike gets the stars variety after being hit on the head by a club in the season four episode "Grand Chef Auto."
In one episode of Wayside, Todd sees stars after a fall. Mrs. Jewls then told Todd to get his head "out of the stars," and it turns out that the stars were really on a project involving a globe.
In the Batman: The Brave and the Bold episode "Emperor Joker", after Jokermite hits Batmite over the head, Batmite sees bats circling his head. Later, after Batmite knocks out Jokermite, the latter sees flying joker fish circling his head.
In the Earthworm Jim episode "Queen What's Her Name" after Princess Whatshername throws Queen Slugforabutt against a wall, the queen sees little winged Earthworm Jims circling her head.
Used fairly frequently in Kick Buttowski, usually with stars or just a plain circling line. The hard-luck Kick is the most frequent victim. In the episode "Free Gunther," he experiences it about a dozen times in a row while sustaining repeated blows from Magnuson's hammer.
In the Rugrats episode "Reguarding Stuie" after Stu hits his head on a robot duck weathervane and falls off the roof he sees stars and ducks spinning around his head.
The WWE's kid-friendly series of animated shorts "Slam City" uses the stars version on occasion. CM Punk, for example, see circling stars during his battle with The Miz.
In the "Frapp Attack" episode of The Cleveland Show, Cleveland Jr. remarks that he'd rather get hit with a mallet than attend Duke. He proceeds to hit himself, and as birds circle his head, he adds that his preferred sport is bird-watching.
CM Punk (or, more accurately, CM Punk Rock) hears birds and sees stars after Barney knocks him headfirst into a turnbuckle in "The Flintstones and WWE: Stone Age Smackdown."
The VeggieTales in the House episode "Laura at Bat" had this happen to Jimmy Gourd after getting beaned in the head by a ball while he was announcing the climactic ball game. In this case, however, he sees baseballs circling his head.
The House of Mouse short "Donald's Goofy World" has Donald being knocked out with tiny Goofy heads going "A-hyuck!" circling over him. When he regains consciousness, he kicks them away.
At the beginning of the 1963 Disney TV special Inside Outer Space, Professor Von Drake falls off his high seat wiole stargazing from his observatory and lands on the floor, getting stars over his head.
Von Drake: I don't know about you, but I just saw stars I've never seen before!
In the Woody Woodpecker cartoon "The Barber Of Seville'' when Woody shrinks an Indian Cheif's headdress he chases Woody with his tomahawk trying to scalp him, Woody responds by hitting him on the head with a mallet he then sees little birds with turkey feathers on their heads doing the stereotypical war whoop.
On Dragon Tales, Zak gets spinning stars around his head around the beginning of "Calling Dr. Zak" after he and Wheezie shoot out of their knuckerhole really fast and land right on their bottom.
In "Betty Boop's Halloween Party" a party guest is hit in the head by an apple on a string and sees one big star, while a gatecrasher sees multiple stars when devil ghosts hit him with their pitchforks.
On Nature Cat, when the Talking Animal characters are walking through the woods on the way to a Talking Blue Jay's music concert, Nature Cat gets bonked on the head and sees circling blue jays.
In the Family Guy episode "Tales of a Third Grade Nothing", Peter predicts a grand piano will fall on his head. About a minute later, it happens. Peter sees stars when this happens.
Peter: If you get a fourtune cookie, don't open it!