Blindfolded Vision

You could say she's... cross eyed! *Oh-hohoho!*

The self-imposed version of being a Blind Seer. A sighted character who has Blindfolded Vision can see just as well, if not better than if they weren't blindfolded. The reasons for this vary, a Mentor teaching their student that Your Eyes Can Deceive You may take it to the next level, invoking Disability Superpower and complementing it with Charles Atlas training to grant Super Senses, freeing the student from the tyranny of sight. Another possibility is the character's Psychic Powers and Third Eye are enhanced with sensory deprivation, or the blindfold is itself a powerful artifact that confers sight beyond sight a la X-Ray Vision.

Perhaps the most terrifying option is that the blindfold is a self imposed handicap to keep an eye-related power under control. When the blindfold comes off, people fall down. Most importantly, Blindfold Vision provides copious quantities of cool.

Examples of Blindfolded Vision include:

Anime and Manga

Akira does this with Go in Hikaru no Go, when upperclassmen trying to haze him force him to play three simultaneous games while blindfold. Akira reads the flow of their games, rather than memorizing their moves, and schools two of them (although the terrible play of the third throws him off until the blindfold comes off.)
Kaede the ninja in Mahou Sensei Negima wears one while taking down a dragon. Then again, she rarely uses them in the first place.
Aria from Fairy Tail uses the Power Limiter variant but gets Curb Stomped regardless.
Ragnarok the Animation: The party wizard has a blindfold on "to see the truth" relying instead on hearing/second sight to fight. She later wears it on her arm to remind her that the "truth" she believed was actually a deception by her master.
Koyo Aoba from Katekyo Hitman Reborn has completely blacked out sunglasses that function as a Power Limiter, but only manages to fight Ryohei to a draw.
Himuro Hikaru of Dragon Drive does this in the second half of the manga

Comic Books

Cyclops of the X-Men has edged into this on occasion, usually after losing his visor in circumstances where "blast everything in sight" is not a viable option. Notable examples include the occasion when he beat up six men with his eyes shut... while counting every step he took so he could find his way back to his fallen glasses, and his first confrontation with Cassandra Nova.
The Veni-Yan monks in Bone wear hoods that cover their faces, allowing them to concentrate on their Dreaming Eye - giving them the ability to locate things without them being in sight.

Film

Star Wars Episode IV has Obi Wan putting a helmet with the blast-shield down on Luke to teach him to see with the force.
Ty Webb in Caddyshack demonstrates this with a blindfolded golf shot across water onto the tee. Danny Noonan, the protagonist then attempts the same shot and hits into the water.
In the sudden death round of DodgeBall: A True Underdog Story.

Cotton McKnight: In 23 years of broadcasting I thought I'd seen it all, folks. But it looks like Peter LaFleur has actually blindfolded himself.
Pepper Brooks: He will not be able to see very well, Cotton.

Literature

The seeresses of Kell in David Eddings' Malloreon must be blindfolded at all times. Removing the blindfold also robs them of all their powers.
Spook in the final book of the Mistborn trilogy. Roughly two years of using his Super Senses powers non-stop had actually warped his body that he needed it to simply function during the day because his vision was just that good. He isn't even rendered blind, he can see through the tiny holes in the fabric and still assemble a picture with better vision than normal people.
The titular character in The Wonderful Story Of Henry Sugar And Six More was taught to see through things by a guy who did this for a living.

Live=Action TV

One episode of Angel has a human psychic ninja assassin who is telekinetic and fights with a blindfold. ... and he's taken down like a chump by a gaggle of vampires during his big entrance.
On Star Trek: The Next Generation, officer Geordi LaForge was born blind, but can see thanks to a cybernetic implant. His vision vastly outstrips the capabilities of his fellow crewmen.

Tabletop Games

In Dungeons & Dragons there is a magic blindfold that gives you 120 ft bindsight.
- Also, there is a feat/skill for warriors that allows them to fight blindfolded at half the penalties they would normally suffer. It doesn't seem like an advantage at first, but to put it another way, in total darkness, a fighter with this feat would be a lot deadlier than those without it.
The Perfection of the Visionary Warrior. With this ultimate technique in melee combat, the Sidereal wraps a prayer strip around his eyes, which begin to bleed under the magic of the blindfold. The character takes damage and loses physical sight, but he is now able to see the immediate future of the battlefield. This allows him to defend against attacks that have not happened yet and attack during opponents' future openings.

Video Games

Rider from Fate Stay Night. Power limiter variety. If she were to take them off, she could accidentally petrify everyone around her.
Any Nethack character with telepathy can be one of these. In fact, intrinsic telepathy only works when you're somehow blinded, as if the developer team was trying to invoke this trope.
- Playing blindfolded even became an unofficial Self-Imposed Challenge, the "Zen conduct". It is very, very hard to pull off.
Riku of Kingdom Hearts wears a blindfold in order to suppress the darkness inside of him. He still manages to be an excellent fighter regardless.
Demon Hunters in Warcraft are ritually blinded so that the far superior "demon vision" can take precedence.
Guild Wars Ritualists are also blindfolded (or at least, have their eyes covered), to gain a better sense of surrounding spirits.
- In a bit of Fridge Brilliance, Ritualist attacks always hit, but they move as though they have no idea how silly they look.
Zato-1 gave up his sight to gain a beast made out of his shadow. The asskicking he gave people seems to be unblinded.
- It appears that Eddie, the beast, does the seeing for him. When Zato-1 dies and Eddie takes over his corpse, this is specifically the case.
Kreia from Knights of the Old Republic 2 actually is blind but it's self-imposed: she could fix her eyes any time she wanted, but feels she sees better without them.
When Rise of Persona 4 summons her Persona, it puts its hands over her eyes; said hands look like a metal blindfold when joined. Her Persona's power is to sense and examine Shadows from a great distance.
Satsujinki, what Shiki might become in the future, has to bandage his eyes because his Mystic Eyes are so powerful his glasses don't work anymore. He can assassinate Dead Apostles in seconds.
The Edutainment Game Troggle Trouble Math has enemies like this on the sixth level.
The Pokemon Uxie has the power to wipe the memory of anyone who looks into its eyes. As such, it keeps its eyes closed, being able to see things anyway given its psychic abilities.
Kenshi from Mortal Kombat : Deadly Alliance.

Web Comics

In Dominic Deegan Sigfried currently.
- Also the infernomancer in the beginning, later on the blindfold was revealed to have inward spikes.
In Drowtales, male Kyorl'solenurn warriors who accompany a female Warden tend to work blindfolded to rely entirely on their Aura Vision.
- Shan'naal even fires a bow while blindfolded... of course, said bow has an eye.
- Kyorl inquisitors (like the one on the page picture) are basically magic radars on legs. Wearing blindfolds keeps them from being distracted by sight.
Order of the Stick's Sangwaan wears a blindfold at all times. Her job is to act as Azure City's Enemy-Detecting Radar, providing detailed intelligence on incoming enemy forces, and detecting invisibility. She gets eaten by an invisible dragon. Oops.
In Those Destined, members of the most powerful seer order wear blindfolds. They're also those who react the most to the heroine's Chosen One aura.
In Rusty and Co. Madeline always fights with closed eyes. This doesn't seem to impair her performance.

Web Original

The Mask of Justice from the Global Guardians PBEM Universe game has vision powers that only work when he has something opaque covering his eyes, such as his eyeholeless mask.
Spoofed by Spoony when reviewing the old FMV shooter Microcosm. After getting frustrated with the game's Nintendo Hard-ness, he takes a page from Star Wars and blindfolds himself. Amusingly enough, doing nothing but dodging while blindfolded actually worked for him.

Western Animation

Spoofed in SpongeBob SquarePants, when SpongeBob was forced to learn to drive blindfolded and succeeded, but was unable to drive without it.
The Penguins of Madagascar episode "Hidden" begins with the penguins training to fight blindfolded. The only one to fail was Kowalski, who, being The Smart Guy, was unable to turn off his brain and use his instincts. He eventually gets it right after all the others are taken by mysterious captors hidden in the reptile house. They turn out to be friendly chameleons, who were too shy to invite the others to their housewarming party.
Samurai Jack does this, when Jack is nearly killed by three blind archers with superhuman accuracy guarding a wish-granting well. Cue flashback to Jack as a young man learning to fight a group of monks based on hearing alone. After blindfolding himself and spending a minute or two listening to the forest, he's ready to 'fight on their level'.
In the Avatar: The Last Airbender episdoe "The Runaway," Aang invokes this trope because he's learning seismic sense from Toph so he uses his headband as a blindfold.
In G.I. Joe, Jinx was trained by a blind martial artist, so she fights better with her blindfold on than with it off. When she's not wearing her blindfold, her commanding officer(s) tend to yell at her to open her eyes.

Real Life

Real Life martial artists sometimes do this in close contact combat training, working by sense of touch. A youtube search for "blindfolded chi sao" brings up numerous examples.
Various orientation exercises done while blindfolded are standard practice for personal development coaches' lessons. They rely on the fact humans can just as well use all five senses equally, but are conditioned by culture and way of life to rely on vision mostly and ignore the information which comes by other ways - which comes into play when vision is blocked.
Driving or doing other things while blindfolded is a standard magician's trick, though sometimes (especially the knife throwing trick) it's simply done using a fake blindfold.
- For example, Kuda Bux
- According to David Frost's Book of the World's Worst Decisions, on April 13, 1977, some chick named Yvonne Whittlesham who billed herself as "The Psychic Escapologist" decided to celebrate the Queen's Silver Jubilee with a 60 MPH "Blindfold Dash" using an iron blindfold. She crashed into a barn after about four hundred yards.