Survival of the Fittest has a couple of these moments. On the V3 island Bobby Jacks puts his designated weapon (a syringe) to use by sticking it straight through the eye of Tyson Neills. Shameeca Mitchell also killed Boxer Carvalaho like this, with a customised toothbrush/dildo, by stabbing him through the eye and then smashing his head in with a wrench. (No, seriously)
JR Rizzolo's torture of Laeil Burbank, during which he cuts out her left eye with a sword and crushes it with his bare hand.
In SotF Evolution, Billy-Jay Clarke's power is of 'Ocular Luminescence' (torch beam eyes, effectively). However, the feedback loop of said power is flawed and he absorbs so much solar energy that it overloads and his eyes melt.
A particularly squick Eye Scream occurred recently in V4 when Maxwell Lombardi jams both his thumbs into Daniel Blessing's eye sockets... Ouch.
Rekka Saionji is on the receiving end twice in the same post, in the same eye, first from his opponent's elbow, then from his tooth.
SCP-372 ("Peripheral Jumper"). SCP-372 is an example of He Who Must Not Be Seen and tries to avoid being seen. During one experiment where it was released into a room with 4 human observers, it attacked one of them and caused them to lose an eye so they couldn't see it.
SCP-400 ("Beautiful Babies"). SCP-400 is an anomalous form of the common pillbug that enters the body of a human baby by burrowing through its flesh. One possible point of entry is the baby's eyes.
SCP-525 ("Eye Spiders") is a creature made of spider-like legs that band together to seek out creatures, extract their eyes and lay eggs in their sockets.
SCP-679 ("Eyerot"). SCP-679 is a fungus that infects victims, blinds them and replaces their eyes with the fungus.
SCP-819 ("Vital Suckers"). When a blue SCP-819 is consumed the liquids in the eater's eyes are sucked out (causing permanent blindness) and transferred to the eyes of another person. The recipient's eyes burst from the increased pressure and may become dislodged from the eye socket.
SCP-881 ("Little People"). The miniaturized human beings managed to escape confinement and infiltrate Dr. Dammer's body. The end of his That Was the Last Entry is "whsts in my eye" and a string of random letters indicating pain and a loss of control due to their attacking his eye from the inside.
SCP-1013 ("Cockatrice"). After petrifying a creature, SCP-1013 eats the soft tissues of the victim first, such as the eyes.
If SCP-1078 (a small glass eye) is placed over an existing living eye, it causes intense pain in (and loud screaming by) the recipient. The recipient will try to kill themselves as soon as possible to stop the pain.
If SCP-1078 is implanted in an empty eye socket, a number of months later the recipient will begin to suffer audiovisual hallucinations and try to kill themselves, sometimes by ripping SCP-1078 out of their eye socket and dying due to the resulting cranial hemorrhage.
SCP-1344 ("Eye-Catching Goggles"). If a human being puts these goggles on, five seconds later two needles will enter the wearer's eyes and enter the optic nerve. If the wearer removes the goggles the needles will pull their eyes out of their sockets.
SCP-1407 ("DJ's Headphones"). If a human being with SCP-1407 inside its body is exposed to sound above 115 dB, the tissue of the victim's eyes will begin to flake off or dissolve.
SCP-1429 ("Organoid Organisms"). In one case SCP-1429 infected a victim's eye, causing intense pain and blindness. Then the victim's eye muscles were dislodged from their face and their eye (now a grown SCP-1429) escaped from their eye socket.
SCP-1569 ("Jumbo Shrimp"). While the human D-156912 was trapped inside SCP-1569, tendrils inside SCP-1569 destroyed his eyes while trying to interface with them. He could feel his eyes pop and feel goop flowing down his face.
SCP-1616 ("Nibbles"). In one test SCP-1616 teleported the eye of a human test subject into its mouth and nibbled on it. The victim was screaming and begging for help the whole time.
Has happened several times in AJCO; it appears to be a favourite tactic of A_J.
Breyos had a plate of highly infectious and most definitely lethal Wither matter shoved into his eyeball after he insulted A_J's recently deceased dog Holarctic. To add to the scream factor, he then had to have the eye removed to prevent the rest of him from being Withered away. He chose to stay conscious while Clovis yanked it out.
Shortly after, A_J drove Hector's cigar into his own eye because he was annoying her. Fortunately for him, he could simply grow it back whenever he wanted - though Req was understandably rather freaked out when he decided to do it in front of her.
In a rare example not caused by A_J, Mei has only one eye left and a pitch black empty socket on the other side after being spat out by the Void.
Similar to Mei, Ziek wandered back to AJCO after being missing for several months with one of his eyes torn out and constantly oozing blood. Nobody knows what happened to it and nobody will ever find out, as he's been devoured by the Void, but it looks painful.
Xinjao O'Reilly in Tech Infantry loses an eye to a soldering iron during a torture session after being captured by the religious fanatics of the Christian Federation.
Ruby Quest. So much, it's almost a central feature.
The short vid Spider... one of the few cases where it is well earned.
Gaia Online recently introduced the ability for Avatars to purchase new eyes... from the Hair Salon.
Vanessa: Doing eyes isn't too different than doing hair, I guess. Just a lot of snipping and drying and jars of blue stuff.
Older than that is the Oculus Mythica, an item that gives you a bunch of unique eye designs to choose from. Including empty, bleeding eye sockets. Funny, people don't approach me often when I wear that item.
In Mur Lafferty's podcast fiction series Heaven, a character named Daniel loses the same eye repeatedly during the course of the series.
Jordan Eats Normally Now, of The Fear Mythos, has an all-but-shown case with Nathan in this video. You can see Sam grab a pencil, you can hear disgusting squishes in the struggle, and you can hear Nathan shout "MY EYE!" note Later entries confirmed he was stabbed in the eye. He showed up later with an eyepatch, too, which was awesome.
Fivesecondfilms made a series of films (all 5 seconds long) dedicated to eyes and, more often than not, the mutilation and/or removal of them. Check it out here. Don't worry, it's nowhere near as horrific as it sounds.
The character of Galaxy from Equestria Chronicles accidentally teleported her eyeballs out as a foal.
This picture pulls it off in a creepier way than most ever want to see.
Tokyo Magic Star: In episode 4, Sakura attacks a villain with magic. Seems standard for a Magical Girl... until it makes his eyes bleed.
On the Ask Hobo Pony blog, the eponymous character has a glass shard stuck in her eye that she doesn't notice until commentors point it out. She's given a choice of a lollipop, a pencil, and a pair of tweezers to remove it; rather than make the obvious choice of the tweezers, she tries to use the pencil to dig it out which exacerbates the problem when it also gets stuck, so she has to go to a free clinic to get both the pencil and the shard forcibly pulled out.
Chef Pee Pee suffers it in "Bowser's Cookies" when Toad stabs his unprotected eye with a knife and tries to fix it with a Band-Aid. Happens again in the same episode at the end when Bowser sticks a fork into Chef Pee Pee's other eye apparently rendering him unable to see, but he somehow recovers in the next episode.
Chef Pee Pee suffers it again in "Bowser Junior Goes To Disney World!", after Junior finds the knife in a box of Doofy-O's that wins him a trip to Disney World.
Chef Pee Pee suffers it yet again in "The Drone!" and ends up with one of his eyeballs out of its socket.
Bowser Junior suffers it in "Bowser Junior's Happy Meal", when Chef Pee Pee tricks him into playing a game with the pair of scissors he tries to pass off as a Happy Meal toy.
Bully Bill suffers it in "Bowser Junior Learns Karate!", when Junior uses chopsticks under the advice of Jackie Chu.
As the puppets rot in the second episode of Don't Hug Me I'm Scared, the Duck Guy's eye can be seen to have detached from its socket.