This describes a character who appears to have their eyes shut constantly, except, perhaps, for a few instances of surprise or shock. Nevertheless, they still give every indication of being able to see - which implies that this characteristic is actually more of a pronounced squint.
This is an old device to imply wisdom; more recently, it's been subverted as a device to show "wise guys." This device, when used as such, is called "kitsune No me" in Japanese ("fox eyes" or "shifty eyes" in English).
A common variation of this trope is to make the character close his or her eyes into an arc rather than a simple horizontal line. Characters whose eyes are fixed in that position are generally optimistic and almost always unconditionally happy, but more often down-to-earth instead of ditzy. These characters may be prone to comic obliviousness, but outright stupidity is rare. The exact way the closed eyes are drawn can add a lot to this trope - representing anything from serenity, dignity, smugness, humor, indifference or even someone trying to fake any of those.
Finally, closed eyes are sometimes used to depict people who are down and out with their lives as a sign of depression.
Where Eyes Always Shut and Beware the Nice Ones overlap, the character's eyes may open when it's time to get dangerous, usually right before unleashing that Limit Break or entering a state of Unstoppable Rage. This is not uncommon among Affably Evil villains; if the villain always puts up a happy facade, expect those eyes to open when the Berserk Button is activated, just before that final transformation or ultimate attack is unleashed. Either way, the character's now-visible eyes may follow other various Eye Tropes as well.
When this trope occurs as a result of the art style, it becomes "Youngblood's Disease", according to Linkara.
Not to be confused with the Stanley Kubrick film, Eyes Wide Shut.
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Anime and Manga
Mao Yasaka in Gundam Build Fighters, occasionally opens his eyes when he gets serious such as when he fires his Hyper Satellite Cannon.
Gin Ichimaru in Bleach. He has only been seen opening his eyes on very rare occasions, once when attacked, once when attacking, and during his final confrontation with Aizen. Also, if artworks count, the cover of one of the manga issues depicts Ichimaru with his eyes open.
Genryusai Shigekuni Yamamoto also keeps his eyes shut, except when he wants to show he's serious (or seriously surprised).
Captain Unohana of the fourth division closes her eyes, and all smiley, utters a threat (as perceived by her victims), occasionally opening them to emphasize her scariness, when she is trying to intimidate them. Does it work? HELL YEAH!
The flame dragon Setsuna in Flame of Recca literally keeps his single eye closed. If he opens it, anyone who sees it is instantly annihilated.
Chizuru in Squid Girl keeps her eyes closed constantly. She only ever opens them (revealing that yes, she does have eyes) to give Squid Girl a terrifying Death Glare. This, along with Killer Whales and Sanae are the only things Squid Girl is genuinely terrified of.
However, later on (second season of the anime if you're watching that), Chizuru opens her eyes and smiles at Squid Girl perfectly normally because she wants her to be friends with them. It actually goes really well for once until Squid Girl off-handedly mentions that she can go back to being a monster now. The last thing we see of Squid Girl is her being dragged off for another "talk".
Imayoshi Shouichi in Kuroko No Basuke keeps both his eyes closed, and only opens them when he wants to emphasize his words. They're usually very biting against his opponents and condescending, at which point he allows the reader and the characters to glimpse the "worst personality" that characters like Daiki Aomine and Hanamiya Makoto have earlier commented that he has.
Master Korin, Bulma's mother and the fat version of Majin Buu from Dragon Ball.
Goku once forces one of Korin's eyes open. All he sees is a fish swimming through water.
His eyes open for a single frame when he gets beaned in the back of the head by Jessie's Arbok in Who Gets to Keep Togepi?.
One of the few women to actually enjoy his constant flirting is the Frontier Brain Lucy/Azami. Upon returning home at the end of the episode, it is revealed that she keeps a group of Pokémon as pets, all with the same squinty eyes implying that her attraction to Brock was due to this feature.
These days, his eyelids are likely to balloon in those situations you'd expect other characters' eyes to do so. A few times when he's being shocked and his body starts flashing, his skull shows the slits instead of circular eye sockets. Make of that what you will.
His eyes also open when he's being bishounen, but all they ever show is basically a glistening squint.
Justified in Black Blood Brothers: Sei is so powerful that he has to keep his eyes shut at all times; the two times he opens them, he kills a bunch of vampires and opens the magical barrier protecting the Special Zone, respectively.
Bunta Fujiwara in Initial D - even while drifting.
In the original series of The Slayers, Rezo the blind priest. However, that's not because he's a trickster so much as because if he opens his blinded eyes, he'll release the fragment of the supreme demon god, Shabranigdo, imprisoned within, a fact he remains unaware of until he heals his eyesight and does so. Another example is the appropriately-named Inspector Wizer.
Rezo's copy too. Why he doesn't open his eyes considering that the story says his eyes were healed is another question. He doesn't have a demon sealed in him like Rezo.
The reason he kept his eyes shut in the anime is simply because Eris tried to fool the Slayers gang to think he's the real Rezo. In the original novel, however, he had a damn good reason to keep them shut even after the gig was up: he had been fused with a mazoku and it caused him to have extra mouths where his eyes should have been. Yikes.
Xelloss "the Trickster Priest" opens the eyes wide (displaying the vertical pupils) and stops smiling when he ceases his tomfoolery and becomes serious. Given that he's the most powerful Mazoku short of godlike Dark Lords, it's not a good sign. And of course, in this case we cannot write off eyes closed by the lower eyelid (sometimes it's clearly visible) as a stylistic choice.
Chichiri in Fushigi Yuugi — he opens his eyes only when speaking seriously.
This is justified. He's just wearing an Eyes Always Shut mask because he has a disfiguring facial scar, including one missing eye. He takes the mask off to speak seriously. (On the other hand, how he makes vivid facial expressions with the mask on the rest of the time, or is able to see, is never explained...)
Koizumi Itsuki (although he opens his eyes much more frequently than most Eyes Always Shut characters), and in a few cases the narrator Kyon, in Suzumiya Haruhi.
Vato Falman, an officer in Roy Mustang's circle. There's also Ling Yao, who chooses to do this voluntarily, along with always trying to smile, due to the fact that, although he's a pretty nice guy at heart, he happens to have "shifty eyes."
Well/interestingly played with Ling, in that when his eyes aren't closed, you know either he means business or there's something seriously wrong. For instance, when he merges with Greed, when Greed is in control his eyes are always open, but when Ling's in control his eyes are often closed except in serious situations.
There's also Fuhrer King Bradley, who keeps his eyes (though one is hidden behind an eye patch) closed the vast majority of the time.
When Bradley opens his visible eye it means he has dropped his friendly persona and let his true, aggressive, vicious self shine through. And if you can see his other eye, start running. Fast. Not that it will help, since the Magical Eye makes him a nearly invincible/unstoppable fighter.
Richard Wong/Mr. Utsumi, Patlabor's sneaky recurring antagonist.
Captain Goto exhibits this trope frequently as well. He fits the trope quite well as he is both wise and cunning, being on top of a situation well before others clue into it.
Vincent Law in Ergo Proxy. Here, the closed eyes seem to indicate passivity and/or weakness, although he opens them with increasing frequency over the course of the series. Early on though, they tend to open in Let's Get Dangerous moments.
Also pays homage to Plato's 'Theory of Forms'. Once Vincent leaves the dome, he opens his eyes to the truth of the outside world once again.
Coincidentally, Vincent Law and the above mentioned Gin both share the same Japanese voice actor.
Yu-Gi-Oh! GX makes special use out of this trope; Professor Daitokouji/Professor Banner usually has his eyes shut, to go with his friendly, approachable, somewhat goofball teacher persona. He eventually reveals himself to be Amnael, one of the Seven Stars, whereupon he opens his eyes - which are Blood Red. They remain open until his defeat, whereupon they close again for the last few minutes before his death. His spirit, when manifest as himself and not a ball of light, still has him with his eyes shut in later seasons.
Wasn't his hair white when he had red eyes? His eyes could've been another color when he had black hair. However, we might have to go to the Hair Tropes for another story.
His oddly-colored hair and eys likely all had something to do with the disease (or curse, maybe) that was killing him (which eventually did).
Both Mitsune Konno (appropriately nicknamed "Kitsune") and Kaede Nagase (from Love Hina and Mahou Sensei Negima!, respectively) do this; the latter is legitimately wise (although Book Dumb) while the former is more of a "wise guy". Also, Kitsune usually appears with only one of her eyes open, and very rarely opening both (if surprised, for instance, like when she learns from Keitaro that he confessed his feelings to Naru).
Kaede opens her eyes to a gleaming slit during the Mahora tournament. The effect is unsettling.
She also has them open in the Chapter 305 during her fight against Dynamis, and she looks pissed.
Mokona used to have its eyes always closed in Magic Knight Rayearth, so it came as a bit of a shock when one of the Mokona Modokis suddenly opened them in Tsubasa Chronicle after sensing one of Sakura's feathers.
Ohno from Genshiken is another passive example - except when she's in otaku mode. Then you get the scary Blank White Eyes. She has normal eyes in the manga.
However, Ohno's fellow cosplayer and later boyfriend Tanaka plays this trope straight, both in the anime and manga. His face is constantly drawn with very little expression except for the closed eyes and slight smile.
Also Gonzy. Turns out this is because he's actually a Coralian who was sent to observe the crew of the Gekko, and opening his eyes would reveal his true nature (Coralians having distinctive rings in their irises, and usually odd coloration as well).
Subverted somewhat in the first episode of Romeo X Juliet. A wealthy socialite with Eyes Always Shut appears to have them LITERALLY shut - he sweeps in unannounced in a scene, plucks the wrong lady from the dressing room amidst declarations of love for "my honey", and proceeds to take her to a ball...all without being aware that he's dating the wrong girl.
The eponymous Zatoichi (both old version and new) is a blind swordsman who walks around with his eyes closed all the time. At the end of the new version, he does open his eyes briefly for an interesting exchange with a mob boss.
Also, there is a comic scene in the new Zatoichi in which he has eyes drawn on his eyelids - so much so, one of the characters gets flustered, thinking he is staring at her.
Ichi is also a blind assassin it's hinted that she's Zatoichi's daughter; at the very least she's trying to find him.
Shusuke Fuji and Renji Yanagi from The Prince of Tennis. They only open their eyes when they're really serious about something.
Yanagi's case is even more extreme than Fuji's; when he fully opens his eyes during a match, his teammates say they had never seen him like that, unlike Fuji who opens his own eyes more or less often. It's even lampshaded in the manga: Kirihara asks him directly how come he can see if his eyes are like that, and Yanagi is so offended by such a dumb question that he slaps him.
Wanyuudou in Hell Girl, but only in his human form; in his wheel form, he appears with both his eyes open.
Digimon's Neemon frequently has his eyes closed. The Japanese card game suggests that he is lazy or frequently sleepy, but in the show he is perfectly energetic. Previous seasons had Gennai for the wise variation.
No, Neemon's fallen asleep at times in Frontier. He's also not very smart, in contrast to Bokomon.
InuYasha has this with the Soul Piper, a youkai that serves as a psychopomp to deceased children, playing with and entertaining their souls until they are prepared to accept death and move on. Its eyes are usually closed, but every time a child's soul does wrong, the Piper's eyes open a bit more, and when they open completely, the child will be Dragged Off to Hell.
Watari from Death Note. Also simultaneously inverted with L who never closes his eyes, even when he sleeps according to one character. And then, in their joint death scene, Watari opens his eyes and L closes them.
Takashi Yamazaki from Cardcaptor Sakura, although he does open them when someone steps on his foot. Chiharu has apparently noticed this, as she remarks at one point that his eyes "are just lines".
Also from CCS, the anime version of Clow Reed, though he had them open in the manga.
The kindly old scientist and inventor Dr. Mayzel from the Spriggan OVA anime movie (Japan 1998). Although you can clearly see his eyes behind his glasses, they're constantly closed and drawn as upturned curves. In contrast, the character looks rather different in the print manga where he wears Scary Shiny Glasses.
Like many classic examples, Zange Natsume of Inu X Boku SS is a tricky character who, when his eyes are shut, generally comes off as silly, only to open them when he's being serious. He actually takes this Up to Eleven because due to his demon heritage he actually has one hundred eyes all over his body which he usually keeps shut and hidden under his clothes, only opening them all when he needs to use his powers to gather information.
In Saint Seiya Virgo Shaka, one of the most powerful Golden Saints, maintains his eyes shut to actually keep his power under control. When Phoenix Ikki finds out, after sorta recuperating from Mind Rape inflicted by Shaka himself, he tricks him into cutting off all of his senses and overpowers him in a suicidal maneuver, winning their fight and earning Shaka's respect for outsmarting him.
Shaka's Lost Canvas counterpart Asmita, however, is blind.
Another big example is Saemon's friend and superior, Hyouma Muroga. Similarly to Shaka, he's not blind per se, but his special powers (reversing people's murdering instincts on themselves, making them commit suicide instead) are so strong that he can't turn them off, therefore he'd rather keep his eyes closed to avoid hurting his allies and loved ones too. His nephew and pupil Gennosuke also has the same power, but is able to keep it at bay so he doesn't need to close his eyes.
Also, there's a small variation in the original novel. Hyoma is able to control his powers, but can't open his eyes unless it's at night because they're light-sensitive to the point of pain.
Another variation, in both manga and anime: the Igas possess a special cream named "Seven Days Ointment" that seals the user's eyelids completely for at least seven days, forcing them to keep their eyes closed. Both Gennosuke and Oboro are affected by it: Gennosuke has a dose of it thrown at him by Hotarubi, whereas Oboro rubbed some on her own eyes to not use her abilities on her own clansmen.
Naruto usually closes his eyes when he's concentrating his chakra or thinking (for some reason, he has them closed for nearly all of the second episode!). It also adds to his fox-like appearance. Perhaps as a result of Character Development or just Art Evolution, he does this less and less as the series goes on.
When Sai is first introduced in Shippuden, he is constantly wearing a phony smile with closed eyes. Despite the fact that he is repeatedly called on it, he doesn't actually stop until he has had sufficient character development.
Akamaru is a dog with always-shut eyes, which succeeds in giving him a somewhat mischievous appearance. This disappears when he takes on human form for the "man beast clone" jutsu, or in very rare moments of extreme surprise.
Chouza Akimichi is another example - until very recently, his eyes have never been shown open - although he's more of a down-to-earth Gentle Giant than a mischievous type like Naruto.
Fujita Goro/Hajime Saitou of Rurouni Kenshin. He actually has naturally squinty eyes (which Sanosuke notes when first meeting him), and they appear closed while Saitou is "acting" as Fujita, which makes him look more like a "nice guy". Once Kenshin recognizes him at the Kamiya dojo, however, this is dropped completely for the rest of the series.
Also, Chou the Sword-Hunter keeps one eye closed at all times except from when starting to lose the upper hand in a fight. Seeing as this is in a somewhat realistic swordsmanship manga, it could be a shout-out to the practice of closing one eye when trying to piss off an opponent. He's basically saying: "You'd be too easy to beat if my perception was normal."
Soujiro Seta's eyes are always closed, except during his freakout due to one of Kenshin's many Talking the Monster to Death speeches. After he appears to be better, they are again closed.
Tae Sekihara's eyes are often closed, although she sometimes opens them when she is distressed. This seems to happen more in the animated version than the comic. Apparently Watsuki really likes this trope.
Ezra from Vandread has these, obviously to emphasize her wise, motherly persona.
Serpico from the Berserk manga. On the few occasions you see his eyes, almost always during a fight, it marks his Let's Get Dangerous moment where he drops the foppish persona. Though in somewhat of a subversion, his motives are always clear and he sometimes goes out of his way to state them.
Pippin had this trademark way before Serpico entered the story, though, and only ever opened his eyes once.
Sort of half-played with Guts. After the events of the Eclipse, his right eye is permanently closed. He seems to still have perfect depth perception, though, considering how accurately he uses knives, his crossbow, and various attacks that require perfect precision.
Luke Stokkart second in command in squad that very uneffectualy chasing after protagonists, seems to be nice, but when one of most dangerous guys in show start threating his captain he show what he is made from.
From Ikki Tousen Dragon Destiny, the incarnation of Zhao Yun, Chou'un Shiryuu, is practically like this. Apparently, while almost every characters always had their clothes torn one way or another, she manages to keep her clothes clean and never torn from attacks, all when she's fighting with eyes closed. She rarely opens them, if she did, it's probably for a brief of time and in a non-combat situation.
Maiza from Baccano! always has his eyes closed, even while being shot.
Additionally, there's Tick, Elmer and Nick (not to be confused Nicholas). Goose looks like his eyes are always shut, but closer inspection shows that they're just really, really narrow.
Benitora of Samurai Deeper Kyo has his eyes shut most of the time, except when he's shocked by something. The English translation of the manga hangs a lampshade on it, but in the Japanese, he's talking about getting laid.
Aside from some of the official art advertising the manga/anime, he only opens his eyes TWICE in the course of eighty-some episodes. They even make fun of it in one strip, in which he wakes up, opens his eyes, and gasps. A caption underneath states "'I tried opening my eyes today!' - Italy".
Made even better during Bloodbath 2011, when one of the requests was that he keep his eyes open. After about ten seconds, all the other characters were freaked out, and Germany ended up covering Italy's face (because he thought it was "toolimpid").
Kinko from Binbou Shimai Monogatari has these, probably to emphasize that she is the older and thus more mature one of the Echigoya sisters.
Kinnikuman: Ramenman. Opens his eyes occasionally, but they're usually closed.
Shouka from Saiunkoku Monogatari. His perpetually closed eyes seem to indicate his wise and easygoing personality. On the rare occasions he's seen with his eyes open, it typically means very bad things for someone, since it indicates that Shouka is appearing in his role as the deadly assassin known as the Black Wolf.
When Hei adopts his "unassuming nice guy" persona, Li Shengshun, he has a broad smile and his eyes are either closed or wide open; but when being his actual self, he has open Mind-Control Eyes and a stoic personality.
Amagiri has one Eye Always Shut, which gives him a cheerful appearance and fits his personality fairly well.
Mocked in Eyeshield 21 with the sumo wrestler Omosadake, who everyone knows has Eyes Always Shut, because he's literally too lazy to open them. They also look nothing like the usual versions, being extremely swollen.
There's also Yamabushi from the Shinryuuji Nagas, whose eyes aren't even slightly cracked when he cries.
One recurring villain from AIKI, a poison user, has her eyes perpetually half-lidded at best. Until Chapter 39 - when Kageyusu knocks her syringe out of her hand, her eyes pop open and remain open.
Saburo Watanuki in Penguin Revolution, another instance of the trope being used to indicate a wise and good-natured character.
In the Area 88 TV series, Roundell not only has an eyepatch but his one good eye is always shut...until he suffers a flashback at in inopportune time and it snaps wide open. Watch out for that cliff!
In the Area 88 manga, Hoover and Ryoko's father are also drawn with their eyes always shut.
Saku, the drummer in BECK always has his eyes shut to the point where they are even joked about in the dub (a life guard refers to him as the one with the "squinty eyes").
Shino from Kannagi, despite having her eyes closed all the time, still manages to be the hottest character in the series. According to her best friend, something bad apparently happens when she opens them.
She opens her eyes when singing, which is stated as the reason why she doesn't sing in the karaoke episode.
Neko-san, from Shinobi Life, is Beni's minor-character-Meido. She never opens her eyes, regardless of when the situation obviously calls for it.
IGPX: Team Black Egg's frontman Ricardo Montazio. One can wonder how he can pilot one of those mechs without having his eyes visibly open.
Koma from Hyakko—not surprising, since she can be seen as an expy of Tamami.
Code Geass: Nunnally Lamperouge/vi Britannia has her eyes permanently closed. Her blindness is said to be psychosomathic, and it's believed it comes from the trauma of witnessing her mother's bloody assassination, which also left her crippled. Telling truths, the specific cause of Nunners's blindness is a Geass-induced trauma, given to her by her father. She 'wakes' up just in time for Lelouch..
Nonohara Kaede from Hayate the Combat Butler was never seen opening his eyes. In addition to his Eyes Always Shut, he's always smiling.
Izumi Segawa's eyes are often shut as well.
Futugami, the Columbo-esque reporter in RahXephon has his eyes shut most of the time, and generally opens them at moments indicating that his seemingly bumbling persona is Obfuscating Stupidity. He also fits the wise and kind elder version.
Chiffon Fairchild from Freezing. Perhaps one of the few genuinely kind, sane people among the crazed, blood-thirsty Amazon Brigade that is West Genetics...and is apparently also the strongest among them, having the nickname "Matchless Smiling Monster".
In Detective Conan, Ayako, Sonoko's older sister, is never seen with her eyes open. (Also, "Sleeping Kogoro's" eyes are always shut when he is "solving the case," though granted this is because he literally is asleep.)
Another prominent character with eyes always closed it Okiya Subaru. When he opens his eyes, he's revealed to be Akai.
Some guest characters are also fox-faced.
In Higurashi no Naku Koro ni, Kimiyoshi almost always has his eyes closed. It's a subject that even his English VA, Kyle Hebert, joked about at an anime convention, comparing him to Brock from Pokémon.
Chizuru from Shinryaku! Ika Musume. Every single time she opens her eyes, terror sweeps whoever she looks at, regardless of species, sex, or age.
It turns out she's just squinting because of bad eyesight. She spends a chapter with them open after she gets contacts, but gives them up when she realizes that having her eyes open all the time makes everyone else nervous.
Tamako from Rinne always has her eyes closed in a cheerful expression.
Minerva in Maken-ki!. She at first tells that she does this because it makes her look "older and wiser". Later we discover that the real reason for this is to limit and hide away her inter-dimensional teleporting ability.
Nekoyashiki in Rental Magica very rarely open his eyes. This is one thing that makes him appear more mysterious.
Saikawa from Gakuen Babysitters, probably to fulfill the regal butler stereotype. Aside from one early instance in the first chapter where his eyes are slightly open, the series hides what he looks like with his eyes open (along with any other expression outside of "neutral"), with one of the characters lampshading this in Chapter 24
In the Ace Attorney Investigations manga, Henry Biden, who plays "Detective White" of the Othello Detectives, typically has his eyes shut most of the time, except when he's surprised, such as when Edgeworth figured out that he wears platform shoes.
Hayami from Minami-ke is usually seen with her eyes closed, most likely to highlight her cunning and mischievous nature.
AmilGaoul of Kiba actually has a reason for its eyes being closed, at least in its first form: it's eventually revealed that until changing into its second and then third form, when it opens its eyes, Amil Gaoul had been asleep, even as it easily defeated Zed's enemies.
The Western ur-example is Captain Marvel (the one who is not Shazam). He's been drawn with normal eyes lately, but for the great majority of his history they were always closed.
The early Joe Shuster illustrations of Superman were also very squinty, which predate Captain Marvel.
Alex Ross continues to draw Superman with squinty eyes. He says its not to give off an attitude or look wise, its just to make him look like he's doing actual work when performing feats of strength.
Jughead, of the Archie comic books and television show typically has his eyes closed. It's referred to on-panel by other characters often, even down to the fact that this should render him blind. (A case of either Lampshade Hanging or Genre Savvy.)
Let's not forget the time when the gang convinced Jughead to open his eyes, upon which he couldn't see a thing due to bright light...
In some stories, though, he has his eyes partially open, like◊ so◊. As is often the case, it's not as dramatic as you'd think.
And don't forget once he was coaxed into opening his eyes for a group photo, only to have everyone else in the shot blink once the photo was taken.
Before the time-travel flashback thing, Lynn Johnston of For Better or for Worse started drawing Japanese character Dawn Enjo with permanently squinted eyes, which she hadn't done before. No one is entirely sure why.
V in V for Vendetta. His "face" is a mask and the tiny eye slits serve to prevent anyone getting so much as a glimpse of his face.
Rob Liefeld's artwork depicts characters so they look like they're always squinting. It is referred to by reviewer Linkara as "Youngblood's Disease".
The Saint of Killers from Preacher has fairly permanently closed eyelids.
Jon's mother from Garfield; she does open them when startled or surprised though.
Beetle Bailey always has his hat (or his helmet) over his eyes — even when showering.
It's lampshaded in one strip, where the chaplain gently admonishes Sarge to see things from Beetle's perspective. The final frame shows Sarge with his hat covering his eyes down to his nose:
Sarge: Here's half of Beetle's problem, right here.
Also lampshaded in one comic which Beetle is shocked and his helmet in cartoon fashion flies off his head only for a second helmet to be under it. The funny thing is, that wasn't even the intended punchline, it was just bonus silliness.
Usagi Yojimbo: Zatoichi parody Zato-Ino, the blind swordspig. Several other characters like Gen, Katsuichi-Sensei, and Priest Sanshobo are "squinty".
The nameless Thief of Abelagot from The Smurfs story "The Jewel Smurfer".
Peanuts: When Snoopy and Woodstock are put into a three dimensional form, like in toys, statues, etc. their eyes will always be closed. This doesn't apply when they're 2D.
The Sphynxes in The Neverending Story are two gigantic statues whose eyes remain closed until "someone who doesn't feel his own worth" tries to pass between them, then they ominously open and shoot lasers at the person. Luckily Atreyu our hero jumps through quickly enough to avoid getting fried.
The Warcraft novels wrote by Richard A. Knaak feature the green dragons doing this, both in drakanoid and humanoid form. in this case it not only symbolizes their wisdom, but also their ability to see through the Emerald Dream. Specifically, they view their presence in the world of Azeroth as them dreaming. Ysera, queen of the Green flight, has opened her eyes three times in recorded history. She can apparently still see though.
Live Action TV
Harry from 3rd Rock from the Sun. French Stewart, the actor who plays him, is naturally "squinty" and rarely has his eyes open more than slightly. This is particularly pronounced when he smiles, and he plays it up for comic effect. Parodied in the first episode:
Harry: I can't see through my eyelids! Dick: Open them! Harry: Oh, they're manual!
He started doing this to overcome stage fright. Now he doesn't feel comfortable not doing it.
Ditto the late Dennis Wolfberg.
And Jimmy Kimmel.
And Renée Zellweger.
Joel on Mystery Science Theater 3000. In the first episode filmed, he actually showed up extremely tired, but the cast and crew liked the result on film; for the rest of the series, Joel was portrayed in a relaxed, almost sleepy demeanor with half-shut eyes and a relaxed, calm voice.
"Sparky" Mortimer, then-10-year-old sports reporter seen on The Late Show With David Letterman, would squeeze his eyes closed for the first few words of anything he said.
Formerly pictured alongside Gin used to be his Expy Hazama from BlazBlue. When we are first introduced to him, he seems like a very minor character in Noel's story, but then he starts revealing his true, more psychopathic nature and by the story's true end he's revealed as the Big Bad, real name Yuuki Terumi. And in the 2nd game we learn that not only is he a Magnificent Bastard, but also a Man Behind the Man as well. He also opens his eyes much more frequently than his predecessor. Still doesn't stop him from being a sexy, BadassSmoothCriminal.
Kliff Undersn in Guilty Gear (he has one eye open in his VS portrait in GG1).
Interestingly, in the Aishas' profile, they are clearly shown blinking, implying that the "shut" look is what their eyes actually look like.
Ini Miney from Phoenix Wright: Ace Attorney always has her eyes shut. Even in her driver's license photo. The Ini we see, however, is actually Mimi Miney, who's impersonating her sister and keeping her eyes shut to fit the role (hers have a very distinctive look). When her facade cracks later in the case, she opens her eyes.
Both ambassadors in the fifth case of Investigations as well. On Alba they signify age and wisdom, on Palaeno they mark him as a cheerful, if a little ditzy person. Of course, in Alba's case, it's a front.
Natsume in the four first four .hack games also displayed this characteristic, in addition to referring to herself in third person at seemingly random points.
Captain Olimar in Pikmin. Along with just about every other Hocatatian.
Crazy Redd in Animal Crossing. He fits the Japanese view of "fox eyes" perfectly (especially since he's an actual fox)—he operates a black market that sells goods for an outrageous price, although you can occasionally find treasures only available in his shop. In addition to high markup, the games from Wild World onward make him the only outlet for paintings... which are frequently counterfeit.
The Happy Mask Salesman from The Legend of Zelda: Ocarina of Time He also opens his on occasion, but only when he's not happy. This, combined with his general creepiness and un-movements (everyone else in The Legend of Zelda: Majora's Mask and Ocarina of Time moves normally. He shifts from one position to another instantaneously.) make him the source of much terror, but he's not presented as being very wise or very mischievous. However, he is well-traveled and a normal guy doesn't carry around quite that many magical masks (then again, Link winds up with a large collection of them throughout Majora's Mask, so maybe he just goes through Termina often and keeps his eyes open...well, figuratively, anyway.) In the end, we don't know much about him.
Also in Majora's Mask are Sakon the thief, who makes off with Kafei's Sun Mask and the Bomb Shop owner's Blast Mask, and Keaton, a cunning, riddle-telling fox.
All green dragons in Warcraft are described as always having her eyes shut, and even if they're up and moving they see the world through the Emerald Dream. In particular, their leader Ysera the Dreamer only opens her eyes for very important occasions, and has only done so a handful of times in all of history. The first known time was when her beloved friend Malorne died in the War of the Ancients. Recently Ysera has kept them open at all times in order to focus on the threat of the Cataclysm and Deathwing, but the rest of the green dragons still keep their eyes shut.
Mentioned in XenogearsPerfect Works as being what she does in order to keep her high Ether power in check. She can be seen with them open during the out-of-Gear battle against all four of the Elements.
There are typically a couple for every game in the Harvest Moon franchise. The trope usually sticks upon those of characters at old age, or apparently girls who are meant to be represented of beauty.
Then there's Toby/Tao from Tree of Tranquility that is neither, but he does fit the "always cheerful" type. However, in his case, eyes that are always shut appear to be a genetic trait: His uncle and cousin have them too, and if he marries Renee, their son Matt has them too. "They say he's got my eyes."
Lyla only opened her eyes once, for like 6 seconds. Go figure, she has Purple Eyes.
Justified for Uxie: anyone who has seen its eyes doesn't remember it. Or anything that ever happened before that in their life.
Brock qualifies in the games as well.
It's amazing that Kenshin, one of the backup dancers in Osu! Tatakae! Ouendan, can dance so well considering that he always has his eyes closed. A Let's Play of the game jokes that he accidentally glued his eyelids shut.
Just about everyone in Full Throttle, though they do open their eyes wide in surprise now and then.
Exit Fate: Angel's eyes are closed in both her portrait and all but one sprite, causing a common misconception among fans that she's blind.
Madotsuki, the protagonist of Yume Nikki. Probably because she sleeps nearly all the time.
Ms. Accord and Lemres from Puyo Puyo never opens their eyes. In the case of Lemres, fan artists try to give him gold or red eyes.
Both Male and Female Healers in Disgaea always have their eyes closed, with the females lampshading it in Disgaea 3.
Female healer (paraphrased): My eyes don't open very often. But don't worry. Even if our eyes meet, you won't turn to stone. Hehehe.
The only time one was seen with her eyes open was in an art piece for Makai Kingdom, which also activates one of the optional map events.
In Valkyria Chronicless, there's Leon Schmidt who never seems to open his eyes, not evening when he's piloting an aircraft...
Hubert Brixham from Valkyria Chronicles II, although it is explained that one of his eyes was infected back when he was a sniper. Having both eyes closed doesn't seem to prevent him from catching one of his students turning around during a test. He only opens his eyes when he's shouting, which is rarely. There's also the clairvoyant Inghild from the same game who is never shown opening her eyes.
Fo in Battle Arena Toshinden. His character select portrait shows him with this, but only for his original color palette and in-game model. Strangely, his alternate colors (each color set for first and second player had unique portraits) display him with his eyes open. The alternate color model still retains the shut eyes.
The Batter from Off is intended to be this way in his dialogue-box sprite, though because of the way said sprite appears, it can be hard to tell if he isn't just wearing eye black or has four eyes.
Snake from Nine Hours, Nine Persons, Nine Doors. In his case, the eyes aren't simply an artistic device—his eyes really are shut all the time, and it's one of the first things viewpoint character Junpei notices about him. He is, in fact, blind. He only opens them three times:
In one of the puzzles, when Seven/Clover/Snake/Junpei spell "pipe" in a cheer-leading fashion. Snake has his eyes wide open as he shouts "Gimme a P and an E!"
In the Safe Ending, Ace tells Snake that he killed Clover - and exactly how he did it - and Snake snaps and his eyes open as he swears to kill Ace. It's actually pretty terrifying.
When they're putting together what happened to Snake, his eyes are open in the still where he's going for the DEAD. Though as it turns out, that wasn't Snake at all.
Two different characters from Morenatsu — Kyouji and Tetsuya. Epileptic Trees notwithstanding, neither character has said or done anything all that treacherous.
Katawa Shoujo has two examples. First we have the eccentric Nurse who never appears onscreen with both eyes open, and only occasionally actually opens his left eye. The other example is Lilly Satou, who doesn't always have them closed, just about half of the time, such as when she's laughing or deep in thought. This is justified by the fact that she is completely blind and doesn't have much reason to open them.
Anja Donlan from Gunnerkrigg Court. Her eyes appear white when she's seen in silhouette; apparently her usual appearance is just a stylized way to show she has small, dark eyes.
Zimmy has her eyes filled with black gunk most of the time, and the dark circles around them make it even worse by giving the appearance that she has no eyes. It's up to you to decide if she's creepier with them closed or open or in-between.
One of Tom's avatars is pretty much the male version of Zimmy's Ugly Cute appearance.
For a long time Munchie Bear from Charby the Vampirate was like this though in his case it was because someone had stiched his eye lids shut. Currently he has one eye always open and one eye always closed.
One wonders where the anachronic Princess from Rusty & Co. gets all that eye-obscuring mascara.
In Dragon City, Rachel is not only known for her squint, but she also gets angry anytime anyone mentions it. Originally it was thought to be because dragons live underground, but later they figured out she was an Asian dragon. To add insult to injury, Rachel's eldest daughter Erin also has a squint, which might be why Rachel isn't the greatest mother to Erin.
Meena's ex-boyfriend-cum-roommate in Questionable Content. Combined with his behavior, it gives him a beatific air.
Simon from Fruit Incest. His mother wore glasses and always has her eyes half closed, so it could just run in the family.
Mr.Kornada in Freefall seems to do it as a matter of arrogance and willful ignorance. Only a major alarm opens his eyes.
The series Magician features a race of people with powers connected to their blood red eyes. One of the characters is a member of this race and keeps his eyes shut at almost all times, under the orders of his master. This is no problem for him since his race are able to see just fine with their eyes shut.
Dorroile in Something Awful's District Bulletin series. Eventually inverted—when he finally opens his eyes, they become constantly wide and unblinking, thus conveying as little expression as they did when closed.
A comical example from Cloudy with a Chance of Meatballs: Flint's dad has a huge monobrow which obscures his eyes for most of the film, but which moves upwards to reveal them on a couple of occasions where he's shocked.
A partial example: Popeye always has his right eye shut, except when in shock. A common explanation is that it was injured in a fight. Wimpy usually walks around with his eyes shut as well.
Cosgrove in Freakazoid! does this. He did open them three times in the series, in "The Cloud" presumably as an effect of the mountain air improving his mood, and in "The Island of Dr. Mystico" in shock at the actions between Freakazoid and Dr. Mystico at the dinner. No reason given why they opened in "The Wrath of Gutierrez", though. Unless food is that much Serious Business (he opened them while ordering food).
In The Smurfs, Sloppy always wears a Smurf hat completely over his eyes.
Similarly, Snoop Dogg's eyes always have a half-closed, stoned look to them. "Weird Al" Yankovic once Lampshaded this in a faux interview with the rapper, where he dared him to open his eye all the way. Snoop couldn't do it.
Singer Andrea Bocelli always has his eyes either completly shut or almost shut due to being blind.
Gilbert Gottfried, though according to him it's a result of having sex with Joan Rivers.
As noted in the description, the concept of keeping your eyes always closed in Japan (as well as having that telltale grin) was in resemblance to the fox creature kitsune, and people used to believe it meant you were possessed by one. It used to be a common diagnosis for mental illness.