Used to be common in 1950s and earlier horror comics. Frederic Wertham's infamous Seduction of the Innocent described and probably named the "Injury to the Eye" motif, giving examples from comics of the time.
Dick Ayers was inordinately fond of eyeballs flying from heads in the horror comics he illustrated for Eerie Publications (not to be confused with the comic Eerie, from Warren Publications) in the 1960s and '70s.
A similar Joker example appears in Birds of Prey, where the Joker details his much beloved gag-gun (that shoots out a metal pole with a flag attached to it that says "BANG!"), puts it right up to a goon's eyeball and says "Wanna see?" then pulls the trigger.
Another Joker example, much like the one above, occurs when The Joker threatens to shot one of his goons, but a flag that says "bang" comes out instead. Said goon relaxes and says "It's not loaded..." right before The Joker pulls the trigger again, and calmly says, "Nope," as the flag gets fired and lodged in the goon's eye.
In one issue Killer Croc challenges Lady Shiva to a fight, she deflects his swipe back at him and he ends up poking himself in the eye with one of his claws.
She just drew me a beautiful house. She drew it with this pencil... The one I've just sharpened. Open your eyes WIDE, Pearl! Beautiful... blue... oh...
One of the creepier villains of The Sandman was The Corinthian, a nightmarish serial killer who escaped from The Dreaming and had toothed mouths in his eye sockets. He feasted on the eyes of his victims. (There's a different kind of eye squick entirely in a different scene — where his shades get knocked off in a struggle and his additional sockets bite the fingers off one of his attackers. Oh, Lord.)
For added eyeball trauma, there was the issue where Doctor Destiny used Morpheus' dream ruby to control the patrons of a diner and eventually drove a teenage girl to stick skewers in her eyes. "I can see the glory!"
As the Sandman Companion points out, nearly every issue has some Eye Scream moment in some form. Gaiman admits being overly fond of/disturbed by the trope.
The Corinthian's own personal spinoff, Death In Venice, has less of this trope than you'd expect. Still, high points include the Russian soldier who the Corinthian swaps an eye with, who gouges out both his own eyes afterward, desperate to get rid of the realization of what the future of his revolution held, and still can't stop seeing it, and Amedeo being possessed, body-switched, something with the Corinthian and suddenly beginning bleeding copiously from the eyes, as the eye-mouths begin to grow in.
The father of DCU character Mister E gouged out his son's eyes with a sharpened spoon for having a girlie magazine under his bed. Is it any wonder the son has issues with women?
Later issues revealed that the pictures were actually of Mister E's sister and their father, but he'd blocked that memory out for one more acceptable to his psyche.
In one of the X-Men books, Wolverine popped Sabretooth's eyeballs with his bone claws He'd lost his adamantium to the latter, complete with closeup.
In another X-Men comic, a pair of demonic sentient Binoculars, vacuum suck out a man's eyes and use them as its own.
In Grendel: Devil's Legacy, child-molesting serial killer and vampire Tujiro saves the eyes of his victims as souvenirs.
In Watchmen, Sociopathic Hero Rorschach takes his first step toward that status as a kid: some bullies, one of them smoking a cigarette, mock him (accurately) about his mother being a whore, then when they start getting physical Rorschach grabs the cigarette and sticks it into the kid's eye.
Spider Jerusalem does the same thing to an obstructive, mouthy Transient in Transmetropolitan.
Early in Psylocke's superhero career, she filled in for her brother as Captain Britain. The tenure didn't go too well and during a fight with her brother's arch-enemy Slaymaster, he stabbed out both her eyes and then proceeded to beat her nearly to death. Mojo later gave her cybernetic eyes, which transmitted what she saw back to him, letting him turn the X-Men's adventures into TV shows, giving him godlike status in his home realm. She kept these eyes for the remainder of her time in her original body, keeping their function a secret.
In Spider-Man miniarc The Other, everyone's favorite wall-crawler gets his own eye ripped out and EATEN IN FRONT OF HIM by Morlun. He gets better.
At the end of "Confessional", Father Tolly commits suicide by putting two pencils to his eyes and headbutting the pew in front of him.
In "Hunger", John and an african shaman "share a vision" - by the shaman plucking out one of John's an his eyes an exchanging them. One could argue that John was hallucinating, the ritual also featuring a herbal drug ("Christ. I hate psychedelics"), but he promptly complains "Why does primitive magic alwasy hurt!"
In "Son of Man", a mob interrogator uses his own nail clippers to.... no, wait. You'd better read this one for yourself.
In the Minds arc of Cerebus the Aardvark, Dave Sim uses the "Injury to Eye Motif" to Cerebus, the main character.
Two Green Lantern Corps storylines, "Ring Quest" and "Eye of the Beholder," has this in spades. At the end of "Ring Quest," Bzzd flies inside Mongul and emerges graphically through his left eye. In "Eye of the Beholder," in which Green Lantern rookies are targeted with psychological warfare, when (spoilered because some people would probably like to sleep tonight) hundreds of eyeballs rain down on their practice area.
Kyle Rayner has a frequent tendency to go for the eyes when fighting his enemies, especially when he can't use his ring.
Shows up in superhero deconstruction The Boys... as a power of one of the two sympathetic superheroes, Starlight, who can emit a flare of blinding light. she uses this power to blind The FlashExpy A-Train in one eye when he tries to rape her.
Wily Pete of Empowered has found that, since he is a walking body of flame, only one part of the human anatomy lasts long enough for him to get his jollies. And one wonders why Thugboy has some issues. Even if you somehow survived this, his load slowly boils your brain.
This happens to Mindf** k when her brother forces her to gouge out her eyes so she'll rely on her powers to see.
Chaos & Control ◊ from The Savage Dragon would hardly be as memorable without the Eyescream. For those too squeamish to look, Chaos is a big, horned monster. Control is a little guy who controls it by sticking its horns into the sphincters he has where his eyes should be.
Rose Wilson, while under the influence of Psycho Serum, gouges her own eye out to prove her loyalty to her father Deathstroke.
Also played straight with the Zombie Priest, who plucked one of his eyes out, then crushed it to a pulp and fed it to the zombie of a pregnant woman to turn her into Mother Corpse, due to his zombie army being decimated and The Buzzard having settled into the graveyard, preventing him from making more. Later, he gets the remaining one gouged out by the Indian man.
Preacher: It's not shown, but the story behind Herr Starr's mutilated eye is enough to evoke sympathy for an often monstrous character... when he was a little boy, the local bullies carved "a star for Starr" into his face with a piece of broken glass.
To be more specific, they cut five gashes around Starr's right eye, which made the shape of a star.
And during War in the Sun, Jesse Custer loses his left eye entirely - God tears it out with his teeth.
In the Planetary issue "The Torture of William Leather," part of the eponymous torture is done with needle lined goggles.
One Bloom Countystrip illustrated the idea that "television is bad for your eyes" by having a monster suddenly pop out of a TV cabinet and suck out Opus's eyes.
In the Hitman/Lobo crossover, Tommy introduces himself to the 'Bo by tapping on his shoulder and calling him "Miss". Just as Lobo turns to kill the bastich who called him that, he gets shot in both eyes.
In an issue of Buffy the Vampire Slayer Season Eight, Willow is being tortured by Warren Mears, the man she killed. He begins by popping at least one eyeball with a scalpel.
In Identity Crisis, Green Arrow sticks an arrow through Deathstroke's blind eye.
Kay from Fables can see every evil thing somebody has ever done. Going by what trope this is, you can probably guess his means of dealing.... And since he's a Fable, his eyes keep growing back, and he keeps cutting them out.
Not shown, but suggested in The Invisibles when the Conspiracy is subjecting King Mob to Cold-Blooded Torture. Sir Giles reads an excerpt from the handbook on how one should take care when removing the eyeball so as not to sever the optic nerve, thereby allowing the victim to see everything.
Marvel's Thor faced huge disasters everywhere, at the Avengers Disassembled tie-in, and sought the wisdom of Odin at the fountain of knowledge. He was told that Odin did not got the knowledge as a birthright, but with a huge sacrifice, his eye... so Thor gouged out his eye to the fountain. Nothing. Following the steps of someone else will not do it! Thor must make a greater acrifice than that! So... goodbye to the other eye.
DCU Anti-Hero Vigilante (not to be confused with the cowboy themed Vigilante that appeared in Justice League Unlimited) gouges out the Face Heel Turned Jericho's eyes to keep him from using his possession powers (which require eye contact with the target) ever again. Vigilante, who doesn't follow Thou Shalt Not Kill, only "spared" Jericho because he had promised Rose Wilson Jericho's half-sister that he wouldn't kill him.
As of Teen Titans #77-#78 during the Blackest Night, Jericho's eyes and sanity were somehow restored...for now.
Several times in the The Punisher MAX comics by Garth Ennis. Castle gouges out Pittsy's eye with his finger, he cuts out Rawlins' eye during torture, and he stabs Barracuda in the eye with a penknife in a fight. Given the brutality of that series, there are half a dozen other instances.
In Punisher Max, during the Kingpin arc, an unfortunate Mook winds up having his skull squeezed until his eyes pop out of their sockets. If that wasn't nauseating enough, readers are treated to several panels of him fumbling around with his eyes dangling by the optic nerve. He eventually manages to get them back into his head just in time to run into The Punisher
One mainstream comic by Garth Ennis has a deranged man paying homeless people to lure other homeless into the sewers and kill them, heaping them into a giant pile of decomposing corpses that he uses like a nest. A fairly level-headed and pacifistic social worker confronts him and is so disgusted and horrified that she claws one of his eyes out in a blind rage. The man doesn't seem much bothered by it.
In one Catwoman story arc where Black Mask had captured the title character's sister and brother-in-law, Eye Scream was just the beginning of the torture that he had in store for them: "Over the teeth, past the gums; look out stomach, here it comes!"
In The Ballad Of Halo Jones, it's apparently standard military training to learn how to put an enemy's eyes out with your thumbs.
A heroic example occurs with Kylun in the pages of Excalibur when the evil Necrom attempts to lure him into a trap with an image of his dead girlfriend. Kylun isn't fooled, and as Necrom is sneaking up behind him to drain his life he lashes out with one of his magical swords, slashing Necrom across the face and putting out one of his eyes. Kylun attacks Necrom, the guy who actually killed his girlfriend in the first place, but the villain sensibly flees the battle.
In The Dead Man, the specteral witch Nausea (an ally of the Dark Judges) burns out a child's eyes in the Cursed Earth by making him think she can actually hurt him. He later has them restored by a thankful Mega City One after the Deadworlders are defeated.
In "The Final Solution" arc of Strontium Dog, Johnny loses his eyes when he tries to scan the Lyran monster to figure out how to kill it and return the mutants to Earth.
In The Walking Dead the Governor suffers a particularly vicious torture fest, including having one of his eyes dug out with a spoon. Later he's shot in the back of the head, which pushes his other eye out.
And then there's the super-disturbing story about a guy who got really stoned and ate his four-year-old son's eyes.
In Sin City, Marv beat Manute so badly that he tore an eye out.
Not as gruesome as the above examples, but in Devil's Due's G.I. Joe vs. The Transformers, Snake-Eyes confronts Starscream, who badly burned Snake-Eyes' face and cost him his voice the last time they crossed paths. Snake-Eyes gets his revenge by slashing open Starscream's optic and shoving a live grenade into the open socket.
Usagi Yojimbo: In the Treasure of the Mother of Mountains story arc, Usagi fights an oversized thug. Usagi manages to gouge the thug's left eye before the thug's buddies overwhelm him and take him prisoner. They continue to trade eye-related insults for the rest of the storyline until Usagi escapes from imprisonment, the thug tries to take him down-and Usagi intentionally slashes out the thug's right eye and leaves him there instead of striking a finishing blow.
Happened once in Johnny the Homicidal Maniac where Johnny was torturing people, one was a guy with his eyes nailed to the wall above him, out of their socket, but still attached to his head.
Deathstroke from the Teen Titans comic lost an eye when his wife shot him for endangering their son Jericho (which led to Jericho getting his throat cut and losing his voice). He loses the other eye in Titans #33. He gets better.
In one story, Superman got a shard of Kryptonite lodged in his eye (among other places) courtesy of Livewire.
Has happened twice to Marvel Family villain Captain Nazi. Catman jabbed him in the eyes with hypodermic needles during Villains United, and when he showed up in the Batman books a few months later with nifty gadgets that let him see, Red Hood blasted them with a stun gun.
Dead Eyes Open has quite a few Returners get shot in the eyes by guns. One scene has a Returner junkie take tranquilizer darts to the eyes to administer a drug (since Returners' hearts no longer pump blood).
ElfQuest's aptly-named One-Eye got his name after a human gouged out the other one with a sharpened stake. Not seen, just referred to as part of his back story. In a later storyline the human warlord Grohmul Djun punishes an inattentive guard by putting his eye out with a shard from the elves' temporarily disintegrated Palace.
Doctor Strange lost his left eye when the demon Ghaszaszh Nyirh blasted it with a bolt of energy. He wore an eyepatch for a while, until Agamotto restored his eye (or more accurately, gave him someone else's).
What, no love for Neil Gaiman's Teknophage? Published by the short-lived Tekno Comix (1995-1997), the titular Teknophage (a 65-million-year-old ruler of many worlds) had a use for every part of a human, including the soul. Before you were tossed into the pit that would presumably render you down for parts, they sucked your eyes out with a vacuum device so you wouldn't have to see what was about to happen to you (the closest thing to 'mercy' that the Phage had.)
In the Topps Comics Zorro, Roman Santiago is blinded when a flintlock pistol goes off in his face, releasing a cloud of superheated gas into his eyes. The results of this are not pretty. It is his blinding that causes his sister Anita to adopt the vigilante identity of Lady Rawhide.
Particularly gory example in Infinite Crisis when Black Adam sticks his fingers through Psycho-Pirate's eyes with such force that he pushes his mask out through the back of his head.
Transformers: Last Stand of the Wreckers: Stalker gets Twin Twist, Impactor and Springer in his lab. When Twin Twist is next seen, his face has been mutilated, one eye is missing, and the other has its lens broken. In the final battle, Impactor harpoons Overlord in the eye, which he shrugged off, and Overlord rips off Springer's face, destroying half his head, including knocking an eye out.
In The Movement, A serial killer called the Cornea Killer is on the loose. The killer murders homeless people and cuts out their eyes as an M.O.
Inverted in the 90s Ghost RiderSpin-OffBlaze; whenever the EyelessBlind Seer Clara puts on the disembodied Kristall-Starrer eyes, they are shown crawling out of their jar and entering her non-existent eyesockets in vivid detail.
In the first issue of Justice League Elite, Menagerie takes a dart to the eye. It's unclear why it doesn't leave her permanently blind in one eye.
In a tie-in comic to the G1 branch of My Little Pony, this is used to explain the "Twinkle-Eyed Ponies" toyline that had been recently released, at that time. Essentially, the Twinkle-Eyed Ponies were originally ponies enslaved by a jewel-obsessed wizard, forced to mine magical gemstones in pitch-black darkness deep below the Earth, where the darkness and/or the light from the gemstones rendered them blind. Though Applejack saved them, in the process, she triggered an explosion that embedded gemstones into their eye sockets. Though this worked out, as it restored their sight, it's still shudder-worthy.
At least one fanfic that mentions this comic, A Mighty Demon Slayer Grooms Some Ponies, notes that the Twinkle-Eyed Ponies eventually separated from the other pony tribes because, to normal ponies, their eyes caused an Uncanny Valley reaction that left them freaked out.
Even that comes from the comic, or at least them fearing that: the next batch of Twinkle-Eyed Ponies from the toyline was intro'd to the comic with the explanation that, until being discovered in that story, they'd stayed in the caves for fear of being seen as freaks by other ponies.
Because Morbiusthe Living Vampire isn't a real vampire, sunlight will not kill him outright, but he is highly sensitive to it. When monster hunter Robert Hellsgaard tortured him, he used a beam of purified sunlight shone in Morbius' eye to get him to spill all of his allies' weaknesses.
Done by the Silver Surfer, of all people. In the most recent Silver Surfer comic series, he's fighting an alien ruler Zed who has supernatural armour and sword from outside the universe. These items make him immune to the Silver Surfer's Power Cosmic. Unfortunately for Zed, the armour has an open face-plate so the Surfer pokes him in the eyes, 3 Stooges style. This being the Surfer, he only gives Zed a really light poke so nothing popped out and he recovered in time to see the Surfer stab him with his own sword.
In issue 1 of Wolverines, Daken has one of his eyes ripped out by Sinister, who takes it along with Wolverine's corpse for research purposes. Ordinarily this wouldn't be an issue for him, but in the last issue of The Logan Legacy, his Healing Factor had been stripped from him by Siphon.
In Zero Carlyle shoves glass in Zero's eye. He just has a hole there now (or in 2018 a glass eye).